Chordal graph

About: Chordal graph is a research topic. Over the lifetime, 12858 publications have been published within this topic receiving 314218 citations.

Graph Theory and Its Applications

Abstract: INTRODUCTION TO GRAPH MODELS Graphs and Digraphs Common Families of Graphs Graph Modeling Applications Walks and Distance Paths, Cycles, and Trees Vertex and Edge Attributes: More Applications STRUCTURE AND REPRESENTATION Graph Isomorphism Revised! Automorphisms and Symmetry Moved and revised! Subgraphs Some Graph Operations Tests for Non-Isomorphism Matrix Representation More Graph Operations TREES Reorganized and revised! Characterizations and Properties of Trees Rooted Trees, Ordered Trees, and Binary Trees Binary-Tree Traversals Binary-Search Trees Huffman Trees and Optimal Prefix Codes Priority Trees Counting Labeled Trees: Prufer Encoding Counting Binary Trees: Catalan Recursion SPANNING TREES Reorganized and revised! Tree-Growing Depth-First and Breadth-First Search Minimum Spanning Trees and Shortest Paths Applications of Depth-First Search Cycles, Edge Cuts, and Spanning Trees Graphs and Vector Spaces Matroids and the Greedy Algorithm CONNECTIVITY Revised! Vertex- and Edge-Connectivity Constructing Reliable Networks Max-Min Duality and Menger's Theorems Block Decompositions OPTIMAL GRAPH TRAVERSALS Eulerian Trails and Tours DeBruijn Sequences and Postman Problems Hamiltonian Paths and Cycles Gray Codes and Traveling Salesman Problems PLANARITY AND KURATOWSKI'S THEOREM Reorganized and revised! Planar Drawings and Some Basic Surfaces Subdivision and Homeomorphism Extending Planar Drawings Kuratowski's Theorem Algebraic Tests for Planarity Planarity Algorithm Crossing Numbers and Thickness DRAWING GRAPHS AND MAPS Reorganized and revised! The Topology of Low Dimensions Higher-Order Surfaces Mathematical Model for Drawing Graphs Regular Maps on a Sphere Imbeddings on Higher-Order Surfaces Geometric Drawings of Graphs New! GRAPH COLORINGS Vertex-Colorings Map-Colorings Edge-Colorings Factorization New! MEASUREMENT AND MAPPINGS New Chapter! Distance in Graphs New! Domination in Graphs New! Bandwidth New! Intersection Graphs New! Linear Graph Mappings Moved and revised! Modeling Network Emulation Moved and revised! ANALYTIC GRAPH THEORY New Chapter! Ramsey Graph Theory New! Extremal Graph Theory New! Random Graphs New! SPECIAL DIGRAPH MODELS Reorganized and revised! Directed Paths and Mutual Reachability Digraphs as Models for Relations Tournaments Project Scheduling and Critical Paths Finding the Strong Components of a Digraph NETWORK FLOWS AND APPLICATIONS Flows and Cuts in Networks Solving the Maximum-Flow Problem Flows and Connectivity Matchings, Transversals, and Vertex Covers GRAPHICAL ENUMERATION Reorganized and revised! Automorphisms of Simple Graphs Graph Colorings and Symmetry Burnside's Lemma Cycle-Index Polynomial of a Permutation Group More Counting, Including Simple Graphs Polya-Burnside Enumeration ALGEBRAIC SPECIFICATION OF GRAPHS Cyclic Voltages Cayley Graphs and Regular Voltages Permutation Voltages Symmetric Graphs and Parallel Architectures Interconnection-Network Performance NON-PLANAR LAYOUTS Reorganized and revised! Representing Imbeddings by Rotations Genus Distribution of a Graph Voltage-Graph Specification of Graph Layouts Non KVL Imbedded Voltage Graphs Heawood Map-Coloring Problem APPENDIX Logic Fundamentals Relations and Functions Some Basic Combinatorics Algebraic Structures Algorithmic Complexity Supplementary Reading BIBLIOGRAPHY General Reading References SOLUTIONS AND HINTS New! INDEXES Index of Applications Index of Algorithms Index of Notations General Index

Graph Coloring Problems

Abstract: Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

Algorithmic Aspects of Vertex Elimination on Graphs

Abstract: We consider a graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations. We give a new linear-time algorithm to calculate the fill-in produced by any elimination ordering, and we give two new related algorithms for finding orderings with special properties. One algorithm, based on breadth-first search, finds a perfect elimination ordering, if any exists, in $O(n + e)$ time, if the problem graph has n vertices and e edges. An extension of this algorithm finds a minimal (but not necessarily minimum) ordering in $O(ne)$ time. We conjecture that the problem of finding a minimum ordering is NP-complete

Domination in graphs : advanced topics

Abstract: LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizations convexity of external domination-related functions of graphs combinatorial problems on chessboards - II domination in cartesian products - Vizing's conjecture algorithms complexity results domination parameters of a graph global domination distance domination in graphs domatic numbers of graphs and their variants - a survey domination-related parameters topics on domination in directed graphs graphs critical with respect to the domination number bondage, insensitivity and reinforcement.

Ribbon graphs and their invariants derived from quantum groups

Abstract: The generalization of Jones polynomial of links to the case of graphs inR 3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum groups.