Graphical Models Models and Bayesian Networks. By Kevin Murphy, 1998. Graphical models are a marriage between probability theory and graph theory. http://www.ai.mit.edu/~murphyk/Bayes/bnintro.html
Extractions: By Kevin Murphy, 1998. "Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering uncertainty and complexity and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms. Fundamental to the idea of a graphical model is the notion of modularity a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data. The graph theoretic side of graphical models provides both an intuitively appealing interface by which humans can model highly-interacting sets of variables as well as a data structure that lends itself naturally to the design of efficient general-purpose algorithms. Many of the classical multivariate probabalistic systems studied in fields such as statistics, systems engineering, information theory, pattern recognition and statistical mechanics are special cases of the general graphical model formalism examples include mixture models, factor analysis, hidden Markov models, Kalman filters and Ising models. The graphical model framework provides a way to view all of these systems as instances of a common underlying formalism. This view has many advantages in particular, specialized techniques that have been developed in one field can be transferred between research communities and exploited more widely. Moreover, the graphical model formalism provides a natural framework for the design of new systems."
Extractions: This inequality does not hold for graphs in general as was shown by Henning, Oellermann, and Swart . It was shown in the same paper that for a graph G and n=3 and 4: diam n n G. It was shown by Oellermann and Tian that for a tree T: C n-1 (T) is contained in C n It remains an open problem to determine whether this containment holds for general graphs. In other words, it is not known if the Steiner (n-1)-center of a graph is contained in its Steiner n-center. It was shown by Beineke, Oellermann and Pippert that if T is a tree, then M n-1 (T) is contained in M n It remains an open problem to determine whether this containment holds for general graphs. In other words, it is not known if the Steiner (n-1)-median of a graph is contained in its Steiner n-median. Oellermann and Tian ). It is known that every graph is the 2-median of some graph (see Holbert ,and Hendry ). Steiner n-medians of trees have been completely characterized by
Bert Gerards - Graph Theory (Math 214) graph theory Part of Discrete Mathematics 2 (Math 214), Victoria University of Wellington Links point to pdf files. Introduction to graph theory Trees http://www.mcs.vuw.ac.nz/~visitor5/
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
Extractions: Burlington VT 05401-1455 USA 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! Classical questions on genus Coloring graphs and maps Drawings and crossings Paths, cycles, and matchings
Graph Theory: Links Around The WWW MCS 125 Class Project Maia Borderaux/Dyuti Sengupta. PRACTICAL graph theory. Link Collection for graph theory. What s wrong? Forget your graph theory? http://www.mills.edu/ACAD_INFO/MCS/CS/MCS125/proj/S00/Practical.Graph.Theory/mat
Extractions: Maia Borderaux/Dyuti Sengupta PRACTICAL GRAPH THEORY Graph theory started in the 18th century around the time Leonard Euler solved the Konigsberg Bridge puzzle by proving that if a connected graph has no more than two vertices of odd degree, then some path traverses each edge exactly once. What does this mean? Let's take a look at the picture... GRAPHS ARE FOR REAL It has only been realtively recently that graph theory has been put to wide practical use. For example in chemistry, where atoms are vertices and the bonds between them are edges or in call graphs which have telephone numbers for vertices and calls made between the numbers constitute edges. OH NO, NOT THE WEB AGAIN! Arguably the most widely known and broadly accessed graph being studied today is the World Wide Web. Although not popularly thought of as a graph, one can consider the different Web pages to be vertices and the links between them to be edges, making the Web a graph. Granted, the Web is an enormous graph; it has some 800 million vertices. It has only been recently that graph theory has been thought to be useful in studying such a tremendous structure. Due to the size of the graph of the Web, studying it requires that one move sections of it in and out of memory and disk storage, a procedure that destroys the efficiency models of most algorithms run on these sections. In order to make the study of such large graphs more accessible, they are reduced from directed multigraphs to undirected simple graphs.
Gordon Royle's Open Questions Colouring, algebraic graph theory, geometries. http://www.cs.uwa.edu.au/~gordon/remote/questions.html
Extractions: This page lists a variety of questions in combinatorics that I believe are open questions and to which I would be interested in knowing the answer. For the moment there is no particular order to the questions, nor any segregation between questions of great difficulty and importance and incremental advances in pushing back the borders of knowledge. Of course this information will change over time - please let me know if you can update any of the information here. Also I am far from being an expert in many of these areas so if you see any blunders or can inform me of any further information please mail gordon@cs.uwa.edu.au This is all very much under construction - besides being lazy, I have a million other things to do. The ultimate reference for open questions on graph colouring is the recent book Graph Coloring Problems by Tommy Jensen and Bjarne Toft. I will just be mentioning some of the ones that I find most appealing (i.e. nothing to do with embeddings or asymptotics), and some that do not appear in GCP. Prove or disprove Hedetniemi's conjecture that the product of two graphs of chromatic number n must also have chromatic number n. See GCP, Problem 11.1.
Stephen C. Locke graph theory and algorithms. http://www.math.fau.edu/locke/
Extractions: Thesis title: Extremal Properties of Paths, Cycles and k-Colourable Subgraphs of Graphs M.Math. ( Combinatorics and Optimization University of Waterloo B.Math. ( Combinatorics and Optimization and Pure Mathematics University of Waterloo , 1975. Putnam competitor for all four years. Our team won in 1974. Married since 1974 to Joanne Thomson Locke . Sons Daniel and Geoffrey ( Jeff Graph Theory and Graph Theory Algorithms, particularly Dirac-type conditions and long cycles, independence ratio in triangle-free graphs. 1995 recipient of a Teaching Incentive Award . Thank you to all the students who wrote letters on my behalf.
Dr. Bela Bollobas Functional analysis, combinatorics and graph theory. http://www.msci.memphis.edu/faculty/bollobasb.html
Ashay Dharwadker's Profile Algebra, topology, graph theory and theoretical computer science. http://www.geocities.com/dharwadker/profile.html
Gordon Royle Algebraic graph theory. http://www.cs.uwa.edu.au/~gordon/
Dan Archdeacon's Home Page Topological graph theory, combinatorics, theoretical computer science. http://www.emba.uvm.edu/~archdeac/
Extractions: last modified January 29, 2004 I am a Professor in the Department of Mathematics and Statistics at the University of Vermont . For more information click on one of the following: Access Dan Archdeacon's e-mail In the Spring '04 Semester I am teaching: Classes at UVM frequently have Mathematica Labs . Mathematica is a product of Wolfram Research Here is the UVM Registar's home page. Return to the top of the page My research interests are in Graph Theory, Combinatorics, and Theoretical Computer Science. I am particularly interested in Topological Graph Theory. I maintain several other web pages. I direct the Editorial Offices of The Journal of Graph Theory (also see Wiley's JGT home page). We run an Applied Combinatorics Seminar . This is a collaborative effort between UVM's Department of Mathematics and Statistics and St. Michael's University Department of
Hubert De Fraysseix - Home Topological graph theory and combinatorics. http://www.ehess.fr/centres/cams/person/hf/index.html
Rich Lundgren's Homepage Applied graph theory and combinatorial matrix theory. http://www-math.cudenver.edu/~rlundgre/
GETGRATS Home Page A research network funded by the European Commission. http://www.di.unipi.it/~andrea/GETGRATS/
Extractions: a Research Network funded by the European Community GETGRATS (General Theory of Graph Transformation Systems) is a Research TMR Network funded by the European Commission, consisting of seven research groups that are listed here together with the corresponding team leader: University of Antwerp - UIA (Belgium): Prof. Dr. Dirk Janssens Technische Universitaet Berlin - TUB (Germany): Prof. Dr. Hartmut Ehrig Laboratoire Bordelais de Recherche en Informatique - LaBRI (France): Prof. Dr. Michel Bauderon Universitaet Bremen - UNIBREMEN (Germany): Prof. Dr. Hans-Joerg Kreowski University of Leiden - RUL (The Netherlands): Prof. Dr. Grzegorz Rozenberg - UNIPISA (Italy) [main contractor]: Prof. Ugo Montanari - UNIROMA1 (Italy): Prof. Dr. Francesco Parisi Presicce The Network Coordinator is Andrea Corradini (Pisa). The aim of the project is to develop a General Theory of Graph Transformation Systems (GTS) by solidifying the use of mathematics in their study and regarding them as the objects of discourse and interest. Particular emphasis will be placed on the comparison, combination, and unification of the various approaches to graph rewriting, where the involved partners have considerable expertise.
Page Of Yves Lafont University of Marseille II Linear logic, lambda calculus, proof theory, term rewriting. Lafont invented the theory of interaction nets, an elegant theory of graph rewriting. http://iml.univ-mrs.fr/~lafont/welcome.html
Logique De La Programmation The Logic of Programming research team is interested in proof theory and its relations with theoretical computer science. The main topic is mathematical interpretation of proofs nets (proof = graph), denotational semantics (proof = function), and game semantics (proof = strategy). Two realisations of this working programm are Linear Logic and Ludics. http://iml.univ-mrs.fr/ldp/welcome.html
Welcome To JGraphT - A Free Java Graph Library A class library that provides mathematical graphtheory objects and algorithms. JgraphT supports a rich gallery of graphs and is designed to be powerful, extensible and easy to use. Open source, LGPL http://jgrapht.sourceforge.net/
Extractions: JGraphT is a free Java graph library that provides mathematical graph-theory objects and algorithms. JGraphT supports various types of graphs including: Although powerful, JGraphT is designed to be simple . For example, graph vertices can be of any objects. You can create graphs based on: Strings, URLs, XML documents, etc; you can even create graphs of graphs! This code example shows how. Other features offered by JGraphT: graph visualization using the JGraph library ( try this demo! complete source code included, under the terms of the GNU Lesser General Public License comprehensive Javadocs easy extensibility.
Charles Stewart Boston University Programming language theory, optimal reductions, graph reduction, linear logic, semantics of logic, formulae-as-types correspondence, continuation semantics. http://www.linearity.org/cas/
Extractions: I am a postdoctoral researcher in theoretical computer science associated with the Institute of Artifical Intelligence at Technische Universitaet Dresden. In the past, I have been associated with the Theory and Formal Specifications group of Technische Universitaet Berlin, the Linear Naming and Computation section of the Church Project at Boston University, the Department of Computer Science at Brandeis University, and the Foundations of Computation section of the Programming Research Group at Oxford University. My research interests include: Programming language theory: Graph transformation: Graph transformation and the design of distributed algorithms;
Extractions: Avi Wigderson (Institute for Advanced Study) In recent years, new and important connections have emerged between discrete subgroups of Lie groups, automorphic forms and arithmetic on the one hand, and questions in discrete mathematics, combinatorics, and graph theory on the other. One of the first examples of this interaction was the explicit construction of expanders (regular graphs with a high degree of connectedness) via Kazhdan's property T or via Selberg's theorem (lambda Topics to be included are: In the 1980's, results from the theory of automorphic forms were used to construct explicit families of Ramanujan graphs, that is, graphs for which Laplace eigenvalues satisfy strong inequalities. These constructions led to the solution of several long-standing problems in graph theory. The graphs themselves are constructed group-theoretically, as quotients of infinite regular trees (the Bruhat-Tits building) by arithmetic subgroups of the p-adic group SL (Q p ) arising from quaternion algebras. Proving that they have the Ramanujan property requires deep results from arithmetic and the automorphic forms. One uses the Jacquet-Langlands correspondence from the theory of automorphic forms to transport the problem to GL(2) and then invokes arithmetical results (work of Eichler and Deligne on the Ramanujan conjecture for classical modular forms). Work on the mixed case SL
26th Workshop On Graph-Theoretic Concepts In Computer Science (WG 2000) The workshop aims at uniting theory and practice by demonstrating how graphtheoretic concepts can be applied to various areas in Computer Science, or by extracting new problems from applications. The goal is to present recent research results and to identify and explore directions of future research. June 15-17, 2000, in Konstanz, Germany. http://www.informatik.uni-konstanz.de/wg2000/