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Topic: List of graph theory topics

Related Topics

Glossary of graph theory

Graph theory

Graph coloring

Ordered tree data structure

Petersen graph

Topological graph theory

Graph rewriting

Tree (graph theory)

Tree data structure

Extremal graph theory

Tree search algorithm

Inverse graph

Graph homomorphism

Planar graph

Graph exploration algorithm

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	Wikinfo \| Graph theory
		Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road.The only information a weighted graph provides as such is (a) the vertices, (b) the edges and (c) the weights.
		Graph theory is also used to study molecules in chemistry and physics.
		Graph theory is the branch of mathematics that examines the properties of graphs.
	www.wikinfo.org /wiki.php?title=Graph_theory (2257 words)

	Graph theory - Wikipedia, the free encyclopedia
		In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection.
		The data structure used depends on both the graph structure and the algorithm used for manipulating the graph.
		Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values.
	en.wikipedia.org /wiki/Graph_theory (1296 words)

	05C: Graph theory
		A graph is a set V of vertices and a set E of edges -- pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets, which is clearly a broad topic.
		A graph may be viewed as a one-dimensional CW-complex and hence studied with tools from Algebraic Topology, in particular, questions of planarity (and genus).
		Determining the genus of a graph is NP-complete.
	www.math.niu.edu /~rusin/known-math/index/05CXX.html (1204 words)

	Aids Graphs -- Recommendations and Resources (Site not responding. Last check: 2007-11-04)
		This graph showing average life expectancy in Africa is misleading because it does not have a base of zero.
		* In graph theory, a graph is an abstract object consisting of vertices (or ''nodes'') and edges (or ''arcs'') between pairs of vertices.
		Category:Graph theory The category is for specific examples of graphs, not for graph theory topics in general.
	www.becomingapediatrician.com /health/2/aids-graphs.html (1365 words)

	DIMACS/DIMATIA/Renyi Working Group on Graph Colorings and their Generalizations
		One of the central topics in graph theory is that of graph coloring.
		Applications of graph theory have led to fascinating generalizations of the notion of graph coloring, with motivation coming from problems of channel assignment in communications, traffic phasing, fleet maintenance, task assignment, and other practical problems.
		Here, we assign nonnegative integer channels to the vertices of a graph so that if two vertices are joined by an edge in the graph, their channels differ by at least two and if the two vertices have a common neighbor, then their channels differ.
	dimacs.rutgers.edu /Workshops/GraphColor/main.html (2333 words)

	FNF: Principle of Shortest Path SOURCE: Shortest path problem - Wikipedia, the free encyclopedia
		Graphs with weights can be used to represent many different concepts; for example if the graph represents a road network, the weights could represent the length of each road[1].
		graph properties are hereditary, which means that a graph has a property if and only if all subgraphs have it too.
		Graph theory is also used to study molecules in science.
	www.hi.is /~joner/eaps/pr_Shortest_Path.htm (1753 words)

	List of Thesis Topics
		Topics for a thesis would include the history of the problem, including the mistakes made in early "proofs", extension of the problem to more complicated surfaces (what for instance happens if the maps are drawn on the surface of an inner tube?), and an explication of the final correct proof.
		The theory of group representations was introduced by Frobenius in 1896 as an attempt to generalize the theory of characters of finite abelian groups.
		The theory of quadratic forms introduced by Lagrange in the late 1700's and was formalized by Gauss in 1801.
	www.middlebury.edu /academics/ump/majors/math/courses/thesis/lists.htm (5244 words)

	The Math Forum - Math Library - Graph Theory (Site not responding. Last check: 2007-11-04)
		A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets.
		Among the topics of interest are topological properties such as connectivity and planarity (can the graph be drawn in the plane?); counting problems (how many graphs of a certain type?); coloring problems (recognizing bipartite graphs, the Four-Color Theorem); paths, cycles, and distances in graphs (can one cross the Königsberg bridges exactly once each?).
		A series of short interactive tutorials introducing the basic concepts of graph theory, designed with the needs of future high school teachers in mind and currently being used in math courses at the University of Tennessee at Martin.
	mathforum.org /library/topics/graph_theory (2440 words)

	Graphical Models
		Notice that, if this graph was undirected, the child would always separate the parents; hence when converting a directed graph to an undirected graph, we must add links between "unmarried" parents who share a common child (i.e., "moralize" the graph) to prevent us reading off incorrect independence statements.
		In theory, this runs the risk of double counting, but Yair Weiss and others have proved that in certain cases (e.g., a single loop), events are double counted "equally", and hence "cancel" to give the right answer.
		Classical control theory is mostly concerned with the special case where the graphical model is a Linear Dynamical System and the utility function is negative quadratic loss, e.g., consider a missile tracking an airplane: its goal is to minimize the squared distance between itself and the target.
	www.cs.ubc.ca /~murphyk/Bayes/bnintro.html (6628 words)

	Unsolved Problems
		An (m,n)-cage is an m-regular graph with girth n and, subject to this, with the least possible number of vertices.
		The bandwidth of a graph G is the minimum bandwidth among adjacency matrices of graphs isomorphic to G.
		A graph G is t-tough if, for every vertex cut S, the number of components of G-S is at most S/t.
	www.math.fau.edu /locke/Unsolved.htm (2911 words)

	Wiley::Graph Theory
		Intended neither to be a comprehensive overview nor an encyclopedic reference, this focused treatment goes deeply enough into a sufficiently wide variety of topics to illustrate the flavor, elegance, and power of graph theory.
		These strands center, respectively, around matching theory; planar graphs and hamiltonian cycles; topics involving chordal graphs and oriented graphs that naturally emerge from recent developments in the theory of graphic sequences; and an edge coloring strand that embraces both Ramsey theory and a self-contained introduction to Pólya's enumeration of nonisomorphic graphs.
		The independence of strands also makes Graph Theory an excellent resource for mathematicians who require access to specific topics without wanting to read an entire book on the subject.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471389250.html (375 words)

	Techno / Programming Language Theory Texts Online
		Part of the reason PL theory and advanced programming languages seem impenetrable to other communities is that learning materials are hard to obtain, or demand a sizeable investment of resources (time, money,...) even if the potential reader is only exploring the subject.
		This list focuses on book-length reference works which treat major topics in programming language theory, mathematical semantics and foundations, particularly texts which have gone out of print.
		Dissertations, theses and technical articles are not really suitable for this list, unless they provide an accessible (or: the unique) introduction to, or tutorial for, a relatively broad and/or important topic.
	www.cs.uu.nl /wiki/Techno/ProgrammingLanguageTheoryTextsOnline (659 words)

	Open Directory - Science: Math: Logic and Foundations: Proof Theory (Site not responding. Last check: 2007-11-04)
		Its thematic is focused on developing the theory and the applications of Linear Logic.
		Proof Theory as an Alternative to Model Theory - Short article by Dale Miller, arguing that logic programming languages should base their semantics on proof theory, not model theory.
		Topics in Logic and Proof Theory - Brief introductions to combinatory logic, the incompleteness theorems and independence results, by Andrew D Burbanks.
	dmoz.org /Science/Math/Logic_and_Foundations/Proof_Theory (351 words)

	Read This: Introduction to Graph Theory
		The authors' goals are to introduce undergraduates to the discipline of graph theory, informing them of the subject — as well as the people who shaped it — and then showing some of its applications.
		The lives of some of the people who have played major roles in the development of graph theory are discussed throughout the text.
		The topics covered in the book are isomorphic graphs, trees, connectivity and Menger's Theorem, Eulerian and Hamiltonian graphs, digraphs, graph factorization, planarity, graph coloring, Ramsey numbers, the notion of distance in a graph, and domination numbers.
	www.maa.org /reviews/IntroGraphThy.html (522 words)

	Advanced Topics in Graph Algorithms
		The course emphasized algorithmic and structural aspects of "nice" graph families, in particular perfect graphs, interval graphs, chordal graphs and comparability graphs.
		In Fall 92 the course was based to a large extent on the classic book of Martin C. Golumbic "Algorithmic Graph Theory and Perfect Graphs' (Academic Press, 1980), and in some parts also on the manuscript "The Art of Combinatorics", by Douglas B. West.
		Interval graphs as a subset of tolerance graphs.
	www.math.tau.ac.il /~rshamir/atga/atga.html (262 words)

	The Math Forum - Math Library - Knot Theory
		An extensive annotated list of links to material consisting of problems in which one starts with a geometric figure (say a polytope) but then considers abstract incidence properties of it rather than its metric properties.
		The mathematical theory behind tying a necktie, with illustrations of the Four in Hand, the Pratt Knot, the Half-Windsor, and the Full-Windsor, and a classification of necktie knots with respect to size and shape.
		Fundamentals of knot theory for a wide range of levels - a variety of activities for exploring knots made from pieces of rope.
	mathforum.org /library/topics/knot_theory (2168 words)

	Math 8863 Topics in Graph Theory, Spring 2006 (Site not responding. Last check: 2007-11-04)
		Long-term plan: Below please find a list of topics that I plan to do at some point, but obviously not all can be covered in a semester course.
		Schnyder's theorem and drawing on a grid, a linear planarity algorithm, Tutte's theorem on the Hamiltonicity of 4-connected planar graphs.
		The graph minor project of Robertson and Seymour, the excluded clique theorem, well-quasi-ordering of finite graphs by the graph minor relation, a polynomial-time algorithm for the k disjoint paths problem for fixed k, applications and open problems.
	www.math.gatech.edu /~thomas/TEACH/8863 (351 words)

	[No title]
		This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs.
		It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.
		This book is written for students who have completed a basic graph theory course and for mathematicians seeking a guide for graph theory and graph modeling.
	www.ec-securehost.com /SIAM/DT02.html (371 words)

	The Graph Theorists' Home Page Guide
		First of all, if you're a graph theorist or some person with strong interest in graph theory (you need not to be a mathematician!), and if you have a homepage but don't find a link to it on this page, please contact me as described above.
		PIGALE is a graph editor with an interface to the LEDA library and with many algorithms implemented essentially concerning planar graphs.
		"Graph Theory and Its Applications" (together with Jay Yellen), "a comprehensive applications-driven textbook that provides material for several different courses in graph theory." This site also provides links to other graph theoretical and mathematical resources.
	www.joergzuther.de /math/graph/homes.html (8736 words)

	List of combinatorics topics - Wikipedia, the free encyclopedia
		A few decades ago it might have been said that combinatorics is to mathematics roughly what irritable bowel syndrome is to gastroenterology — a way to classify poorly-understood problems, and some standard remedies.
		This page is complementary to the list of graph theory topics: graph theory being the part of combinatorial mathematics that is most like a separate discipline.
		Since combinatorial mathematics is effectively the environment for the study of data structures in computer science, there are very many topics that arise there.
	en.wikipedia.org /wiki/List_of_combinatorics_topics (185 words)

	Amazon.ca: Topics in Algebraic Graph Theory: Books: Lowell W. Beineke,Robin J. Wilson,Peter J. Cameron (Site not responding. Last check: 2007-11-04)
		The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry).
		Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book.
		To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory.
	www.amazon.ca /Topics-Algebraic-Theory-Lowell-Beineke/dp/0521801974 (447 words)

	Open Directory - Science: Math: Combinatorics: Graph Theory (Site not responding. Last check: 2007-11-04)
		A Constructive Approach to Graph Theory - Notes on a semiotic approach to constructing isomorphism invariants of graphs by John-Tagore Tevet.
		Signed, Gain and Biased Graphs - List of publications and manuscripts annotated by Thomas Zaslavsky.
		The Vertex Coloring Algorithm - A polynomial-time algorithm for coloring the vertices of a graph with a new constructive proof of Brooks' theorem by Ashay Dharwadker.
	dmoz.org /Science/Math/Combinatorics/Graph_Theory (549 words)

	graph theory - OneLook Dictionary Search
		Graph Theory : A Glossary of Mathematical Terms [home, info]
		Graph Theory : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include graph theory: algorithmic graph theory, algebraic graph theory, geometric graph theory, glossary of graph theory, list of graph theory topics, more...
	www.onelook.com /?w=graph+theory&ls=a (115 words)

	Open Questions: Combinatorics, Graph Theory, and Computation
		A version of this list is at Google, with entries sorted in "page rank" order.
		The problems of traversing a graph so that each edge is crossed exactly once is compared with graph traversal where each vertex is encountered exactly once.
		See also Graph (mathematics), Glossary of graph theory.
	www.openquestions.com /oq-ma004.htm (550 words)

	TEXTBOOKS, LECTURE NOTES AND TUTORIALS IN MATHEMATICS
		The theory of the foundations of mathematics - 1870 to 1940
		Mathematics of Rubik's cube by David Joyner is a good source for discrete group theory with applications to permutation puzzles.
		TeX by Topic the TeXbook of Victor Eijkhout
	www.geocities.com /alex_stef/mylist.html (2524 words)

	Fields Institute - Graph Theory and Optimization
		The Special Year on Graph Theory and Combinatorial Optimization is a joint program between the Fields Institute and PIMS.
		The full program on these two subjects will emphasize recent results, open problems, applications, and connections with other parts of mathematics and computer science.
		Graph Minors and Topological Graph Theory, January 17-22, 2000
	www.fields.utoronto.ca /programs/scientific/99-00/graph_theory (252 words)

	Mathematics
		You may wish to read my curriculum or the list of my papers.
		This is a miscellaneous list of sites of interest mathematics (mostly graph theory).
		Graph theory is dealt with at all levels, form basics to current research subjects.
	www.angelfire.com /mi/raffaele55/math.html (248 words)

	List of graph theory topics - Wikipedia, the free encyclopedia
		See glossary of graph theory for basic terminology
		Tree (set theory) (need not be a tree in the graph-theory sense, because there may not be a unique path between two vertices)
		This page was last modified 11:50, 19 October 2006.
	en.wikipedia.org /wiki/List_of_graph_theory_topics (84 words)

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