101. Graph Theory ICS 2010 accepted paper list is here. List with abstracts is here. Following is a list with links to pdf files. Please leave a comment if I missed any pdf files. http://graph-theory.blogspot.com/

Graph Theory Graph Theory, Mathematics, Puzzles and Fun Stuff !! Monday, November 02, 2009 ICS 2010 Accepted Papers (with pdf files) ICS 2010 accepted paper list is here . List with abstracts is here . Following is a list with links to pdf files. Please leave a comment if I missed any pdf files. If you haven't uploaded your accepted paper on your homepages/arXiv/ECCC please do so. As and when I find new files on the internet, I will update them here. Update : Slides of the talks are available online Are Stable Instances Easy? [pdf] Yonatan Bilu and Nathan Linial On the Construction of One-Way Functions from Average Case Hardness [ECCC] Noam Livne Leveraging Collusion in Combinatorial Auctions Jing Chen, Silvio Micali, and Paul Valiant Guaranteeing Perfect Revenue From Perfectly Informed Players [pdf] Jing Chen, Avinatan Hassidim, and Silvio Micali A New Look at Selfish Routing [pdf] Christos Papadimitriou and Gregory Valiant Symmetric LDPC codes and local testing Tali Kaufman and Avi Wigderson Derandomizing Algorithms on Product Distributions and Other Applications of Order-Based Extraction [pdf] Ariel Gabizon and Avinatan Hassidim Game Theory with Costly Computation [pdf] Joseph Halpern and Rafael Pass On the power of a unique quantum witness [pdf] Rahul Jain, Iordanis Kerenidis, Greg Kuperberg, Miklos Santha, Or Sattath and Shengyu Zhang

102. Http://www.g-scop.fr/~moncelj Identifying codes in graphs, combinatorics, graph theory and computer science. http://www.g-scop.fr/~moncelj/

Click here Click here

103. 05C: Graph Theory Introduction Yes, a longer introduction to graph theory will eventually appear Classified in the MSC as a subfield of 05 Combinatorics, Graph Theory has emerged as a related http://www.math.niu.edu/~rusin/known-math/index/05CXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 05C: Graph theory Introduction [Yes, a longer introduction to graph theory will eventually appear...] Classified in the MSC as a subfield of 05: Combinatorics , Graph Theory has emerged as a related but largely independent discipline. A graph History See e.g. Wilson, Robin J.: "200 years of graph theory-a guided tour" Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), pp. 19. Lecture Notes in Math., Vol. 642, Springer, Berlin, 1978. MR58 #15981. A longer version appeared in book form: Biggs, Norman L.; Lloyd, E. Keith; Wilson, Robin J.: "Graph theory: 17361936" Clarendon Press, Oxford, 1976. 239 pp. MR56#2771 Applications and related fields Particularly regular graphs are related to Group Theory . This includes discussion of automorphism groups, Cayley diagrams for groups, and regular graphs. Many graph-theoretic problems can be solved by exhaustive enumeration; the questions then involve complexity. Further topics in this area are included in 68: Computer Science . (In particular this area of overlap includes topics such as the Traveling Salesman Problem, treated here.)

104. Ashay Dharwadker Algebra, topology, graph theory and theoretical computer science. http://www.dharwadker.org/profile.html

Ashay Dharwadker Born January 1, 1967, New Delhi, India Address: Institute of Mathematics, H-501 Palam Vihar, District Gurgaon, Haryana 122017, India. Website: http://www.dharwadker.org Email: ashay@dharwadker.org Research: Fundamental research in mathematics and its applications. Algebra, topology, graph theory, computer science and high energy physics. Institute of Mathematics Space, Time and Matter, http://www.dharwadker.org/space_time Baltic Horizons, Special Issue on Fundamental Problems in Mathematics, 2010. Higgs Boson Mass predicted by the Four Color Theorem, http://www.dharwadker.org/khachatryan/higgs arXiv:0912.5189 Proceedings of the Institute of Mathematics, 2009. Based on the proof of the four color theorem and the grand unification of the standard model with quantum gravity, we show how to derive the values of the famous Cabibbo angle and CKM matrix, in excellent agreement with experimental observations. We make a precise prediction for the elusive Higgs boson mass M H GeV , as a direct consequence of our theory.

105. Free Online Graph Theory Books :: FreeTechBooks.com Graph Theory The study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. http://www.freetechbooks.com/graph-theory-f67.html

FreeTechBooks.com Free Online Computer Science and Programming Books, Textbooks, and Lecture Notes Register FAQ Search Memberlist ... Graph Theory Topics Views Advertisements Digraphs Theory, Algorithms and Applications Presents a unified and comprehensive survey of directed graphs. Covers theoretical and practical aspects, with algorithms, proofs, and applications of digraphs. Includes more than 700 exercises and 180 figures which further clarify topics. Graph Theory Lessons The entire 23 lessons of Graph Theory that utilizes a java software as an investigative tool. The software can draw, edit and manipulate simple graphs, examine properties of the graphs, and demonstrate them using computer animation. Graph Theory With Applications An introduction to graph theory. Presents the basic material, together with a wide variety of applications, both to other branches of mathematics and to real-world problems. Several good algorithms are included and their efficiencies are analysed. Graph Theory, 3rd Edition This book offers an introduction to the theory of graphs as part of (pure) mathematics; it contains neither explicit algorithms nor 'real world' applications. Graph-Theoretic Algorithms: Lecture Notes [URL's removed] Give the readers further exposure to the design, analysis, and application of algorithms for problems defined on graphs. These notes will study how to recognize various graphs classes, and what problems become easier if we have such a graph.

106. Graph Theory By Reinhard Diestel. Sites offers author and book information as well as a downloadable PDF version of the book. http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/

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107. Graph Theory this is a site introducing various terms and knowledge on graph theory. http://www.graph-theory.net/

Graph Theory Just another WordPress weblog Construction of reliable communication networks Let k be a given positive integer to determine the required connectivity of a graph. Let G be a weighted graph. Determine a minimum-weight k-connected spanning subgraph of G. If k=1, this problem reduces to find a minimum spanning tree. Kruskal’s algorithm can be applied to find such a tree. However if k is greater than one, then the above problem becomes difficult and unsolvable. Only if G is a complete graph in which each edge is assigned unit weight, then the problem has a simple solution. It is an m-connected graph H(m,n) on n vertexes and the structure of H(m,n) depends on the parities of m and n; three cases can be considered Case 1: if m=even, let m=2r, then H(2r,n) is constructed as follows. It has vertexes 0, 1, …, n-1 and two vertexes i and j are joined if i-r <=j <=(i+r)mod(n). Case 2: if m=odd, and n=even, let m=2r+1, then H(2r+1,n) is constructed by first drawing H(2r,n) and then adding edges joining vertex i to vertex i+(n/2) for 1 <=i <=n/2.

108. Oxford University Press: Graph Theory 1736-1936: Norman L. Biggs Two centuries of Graph Theory, by Norman L. Biggs, E. Keith Lloyd and Robin J. Wilson. http://www.oup.com/us/catalog/general/subject/?view=usa&sf=toc&ci=0198539169

109. Graph Theory Glossary adjacent Two vertices are adjacent if they are connected by an edge. arc A synonym for edge. See graph. articulation point See cut vertices. http://www.utm.edu/departments/math/graph/glossary.html

Graph Theory Glossary Chris Caldwell This glossary is written to supplement the Interactive Tutorials in Graph Theory . Here we define the terms that we introduce in our tutorialsyou may need to go to the library to find the definitions of more advanced terms. Please let me know of any corrections or suggestion! A B C D ... Z adjacent Two vertices are adjacent if they are connected by an edge. arc A synonym for edge. See graph articulation point See cut vertices bipartite A graph is bipartite if its vertices can be partitioned into two disjoint subsets U and V such that each edge connects a vertex from U to one from V. A bipartite graph is a complete bipartite graph if every vertex in U is connected to every vertex in V. If U has n elements and V has m , then we denote the resulting complete bipartite graph by K n,m . The illustration shows K . See also complete graph and cut vertices chromatic number The chromatic number of a graph is the least number of colors it takes to color its vertices so that adjacent vertices have different colors. For example, this graph has chromatic number three. When applied to a map this is the least number of colors so necessary that countries that share nontrivial borders (borders consisting of more than single points) have different colors. See the

110. Problems In Topological Graph Theory Web text by Dan Archdeacon with a list of open questions in topological graph theory. http://www.emba.uvm.edu/~archdeac/newlist/problems.html

Problems in Topological Graph Theory Go to the Table of Contents Compiled by Dan Archdeacon List Started: August 5, 1995 Converted to the web: September 1, 1998 Last modified: November 15, 1998 E-Mail: dan.archdeacon@uvm.edu Postal Mail: Dan Archdeacon Dept. of Math. and Stat. University of Vermon t Burlington VT 05401-1455 USA Abstract Do you think you've got problems? I know I do. This paper contains an ongoing list of open questions in topological graph theory. If you are interested in adding a problem to this list please contact me at the addresses above. The spirit is inclusive-don't submit a problem you're saving for your graduate student. If it appears here, it's fair game. If you solve one of the problems, know some additional history, or recognize it as misphrased or just a stupid question, please let me know so that I can keep the list up-to-date. I've taken quite a bit of liberty editing the submissions. I apologize for any errors introduced. Enjoy my problems-I do! Table of Contents Classical questions on genus Coloring graphs and maps Drawings and crossings Paths, cycles, and matchings

111. Graph Theory Graph Theory is a 2005 commission of the New Radio and Performing Arts, Inc., (aka Ether Ore) for its Turbulence web site. It was made possible with funding from the Greenwall http://www.turbulence.org/Works/graphtheory/

112. Regular Graphs Page Tables of simple connected k-regular graphs on n vertices and girth at least g. http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html

Regular Graphs The following tables contain numbers of simple connected k -regular graphs on n vertices and girth at least g with given parameters n,k,g . If a number in the table is a link, then you can get further information about the graphs including adjacency lists or shortcode files. A description of the shortcode coding can be found in the GENREG-manual Most of the numbers were obtained by the computer program GENREG. It does not only compute the number of regular graphs for the chosen parameters but even constructs the desired graphs. The large cases with k=3 were solved by Gunnar Brinkmann (University of Ghent), who implemented a very efficient algorithm for cubic graphs. If you want to compute regular graphs on your own or perhaps try one of the unsolved cases, you can get a free version of the generator. There are executables available for DEC-Alpha SGI Workstations and Linux Win NT PCs. The package genreg.tar contains a makefile for easy installation on any UNIX machine. There is a german and an english latex version of the manual included as well as a short C-programm that demonstrates how to read shortcode files. When using GENREG for your publications, please cite

113. Games On Graphs Overview Graphs are mathematical objects that are made of dots connected by lines. Graph Theory is the branch of mathematics that involves the study of graphs. http://www.c3.lanl.gov/mega-math/workbk/graph/graph.html

Overview Graphs are mathematical objects that are made of dots connected by lines. Graph Theory is the branch of mathematics that involves the study of graphs. Graphs are very powerful tools for creating mathematical models of a wide variety of situations. Graph theory has been instrumental for analyzing and solving problems in areas as diverse as computer network design, urban planning, and molecular biology. Graph theory has been used to find the best way to route and schedule airplanes and invent a secret code that no one can crack. The Big Picture

114. Sandpiles In Graphs An application of cellular automata by Angela R. Kerns. http://www.cs.wvu.edu/~angela/cs418a/cs418a.html

Next: Introduction: Sandpiles in Graphs Sandpiles in Graphs Angela R. Kerns Department of Statistics and Computer Science West Virginia University angela@cs.wvu.edu Introduction: Sandpiles in Graphs Cellular Automata Models of Real Sandpiles The Basic Sandpile Model The Graph ... About this document ... Angela Kerns Thu Dec 5 15:22:37 EST 1996

115. Graph Theory Introduction of Graph Theory. EMAT 6690. YAMAGUCHI, Junichi . In the sprign semester 2005, I take the mathematics course named Graph Theory(MATH6690). http://jwilson.coe.uga.edu/EMAT6680/Yamaguchi/emat6690/essay1/GT.html

Introduction of Graph Theory EMAT 6690 YAMAGUCHI, Jun-ichi In the sprign semester 2005, I take the mathematics course named "Graph Theory(MATH6690)." This course is hard but very interesting and open my eyes to new mathematical world. I have loved study Graph theory and really want you to study this very young mathematics. This field of mathematics can be applied for many issues, rainging from operational research and chemistry to genetics and linguistics, and from electrical engineering and geography to sociology and architecture. What is Graph Theory? Graph theory concerns the relationship among lines and points. A graph consists of some points and some lines between them. No attention is paid to the position of points and the length of the lines. Thus, the two graphs below are the same graph. You can get more detailed information of graph theory at this site (http://www.netipedia.com/index.php/Graph_theory) Basic Terms of Graph Theory a SIMPLE graph G is one satisfying that; (1)having at most one edge (line) between any two vertices (points) and

116. Network Resources For Coloring A Graph Resources for formulating and solving coloring problems. http://mat.gsia.cmu.edu/COLOR/color.html

Network Resources for Coloring a Graph by: Michael Trick (trick@cmu.edu) Last Update: October 26, 1994 Introduction Given an undirected graph, a clique of the graph is a set of mutually adjacent vertices. A maximum clique is, naturally, a clique whose number of vertices is at least as large as that for any other clique in the graph. If the vertices have weights then a maximum weighted clique is a clique with the largest possible sum of vertex weights. A (vertex) coloring of an undirected graph is an assignment of a label to each node. It is required that the labels on the pair of nodes incident to any edge be different. A minimum coloring of a graph is a coloring that uses as few different labels as possible. Clique and coloring problems are very closely related. It is straightforward to see that the size of the maximum clique is a lower bound on the minimum number of labels needed to color a graph. Many problems of practical interest can be modeled as clique and coloring problems. The general form of these applications involves forming a graph with nodes representing items of interest. An edge connects two ``incompatible'' items. The maximum clique problem is then to find as large a set of pairwise incompatible items as possible. The minimum coloring problem is to assign a color to each item so that every incompatible pair is assigned different colors. This document tries to bring together the various resources that are available on the Internet to help in formulating and solving coloring problems.

117. Graph Theory ORNotes J E Beasley. OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). http://people.brunel.ac.uk/~mastjjb/jeb/or/graph.html

OR-Notes J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions A full list of the topics available in OR-Notes can be found here Graph theory Introduction Graph theory deals with problems that have a graph (or network) structure. In this context a graph (or network as many people use the terms interchangeable) consists of: vertices/nodes - which are a collection of points; and arcs - which are lines running between the nodes. Such arcs may be directed or undirected and undirected arcs are often called links or edges. An example graph is shown below. Graph theory is used in dealing with problems which have a fairly natural graph/network structure, for example: road networks - nodes = towns/road junctions, arcs = roads communication networks - telephone systems computer systems foreign exchange/multinational tax planning (network of fiscal flows) Note here that the minimum cost network flow problem (also dealt with in this course) is an example of a problem with a graph/network structure.

118. Home Page Of Signed Graphs List of publications and manuscripts annotated by Thomas Zaslavsky. http://www.math.binghamton.edu/zaslav/Bsg/

The Home Page of Signed, Gain, and Biased Graphs by Thomas Zaslavsky Why is this picture appropriate? Illustration by Hugh Thomson, courtesy of Henry Churchyard Mathematical Bibliography A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas Dynamic Surveys in Combinatorics of the Electronic Journal of Combinatorics. Seventh Edition, 1999 September 22. vi + 151 pp. Download the preliminary 8th edition, vi + 249 pp., in PostScript (2 MB) or PDF (2 MB), or the Tex file A signed graph is a graph with signs labelling its edges. A gain graph has elements of any group as edge labels (called "gains"), with the understanding that reversing the sense in which you traverse the edge will invert the gain. A bidirected graph has both ends of each edge directed independently; it can be regarded as an oriented signed graph. This is a classified and copiously annotated list of all the publications (and suitable unpublished manuscripts, theses, etc.) of mathematical interest related to signed graphs, vertex-signed graphs, gain graphs, and bidirected graphs that I've been able to find and examine and enter into the list. It includes all or part of the literature of signed digraphs, Dowling lattices, combinatorics of root systems, parity of cycles and paths and max-cut problems (these concern all-negative signatures), generalized networks (networks with gains), qualitative matrix theory, quadratic pseudo-Boolean functions, dynamic labeled 2-structures, etc., etc., as well as selected publications on applications to social science (psychology, sociology, anthropology, economics) and natural science (physics, chemistry, biologysorry, no geology or astronomy-yet).

119. Multicommodity Problems Instances and random generators of multicommodity flow and network design problems. http://www.di.unipi.it/di/groups/optimize/Data/MMCF.html

Multicommodity Problems Last update: 25/08/2010 This page provides a collection of instances and random generators of Multicommodity Flow problems. The page comprises: Linear Multicommodity Flow problems, ordinary LPs but challenging due to their size; NonLinear Multicommodity Flow problems, difficult both for their size and the nonlinearity of the objective function; Multicommodity Network Design problems, difficult both for their size and the presence of integer variables; Some links to similar pages around the web; A small bibliography of the articles where the instances have been tested. All instances are packed with "tar" and compressed with "gzip"; these are ubiquitous on unix systems, and available for essentially every other architecture. Once a file f .tar.gz has been downloaded, it must be first decompressed (gzip -d f .tar.gz under unix) and then un-tarred (tar xvf f .tar under unix) to retrieve the original files and/or directories. Files of the type f .tgz are compressed by the tar command, and can be decompressed and un-tarred at the same time (tar xzvf f .tgz). A service C++ class for (MMCF)-solvers

120. Graph Theory Graph Theory Graph theory is a flourishing discipline containing a body of beautiful and powerful theorems of wide applicability. Its explosive growth in recent years is mainly http://www.springer.com/mathematics/numbers/book/978-1-84628-969-9

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