Results 11 to 20 of about 946,691 (269)
Clique‐cutsets beyond chordal graphs [PDF]
Electronic Notes in Discrete Mathematics, 2017 Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (eg, the class of perfect graphs and the class of even‐hole‐free graphs), appearing both as excluded ...
Valerio Boncompagni +2 more
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Characterizing 2-Trees Relative to Chordal and Series-Parallel Graphs
Theory and Applications of Graphs, 2021 The 2-connected 2-tree graphs are defined as being constructible from a single 3-cycle by recursively appending new degree-2 vertices so as to form 3-cycles that have unique edges in common with the existing graph.
Terry McKee
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Further results on Hendry's Conjecture [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Recently, a conjecture due to Hendry was disproved which stated that every Hamiltonian chordal graph is cycle extendible. Here we further explore the conjecture, showing that it fails to hold even when a number of extra conditions are imposed.
Manuel Lafond +2 more
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Algorithms and complexity for geodetic sets on planar and chordal graphs [PDF]
International Symposium on Algorithms and Computation, 2020 We study the complexity of finding the \emph{geodetic number} on subclasses of planar graphs and chordal graphs. A set $S$ of vertices of a graph $G$ is a \emph{geodetic set} if every vertex of $G$ lies in a shortest path between some pair of vertices of
Dibyayan Chakraborty +5 more
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Algorithmic Aspects of Some Variations of Clique Transversal and Clique Independent Sets on Graphs
Algorithms, 2021 This paper studies the maximum-clique independence problem and some variations of the clique transversal problem such as the {k}-clique, maximum-clique, minus clique, signed clique, and k-fold clique transversal problems from algorithmic aspects for k ...
Chuan-Min Lee
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An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs,
Takuro Abe, Koji Nuida, Yasuhide Numata
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Properties and Recognition of Atom Graphs
Algorithms, 2022 The atom graph of a connected graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all its atom trees.
Geneviève Simonet, Anne Berry
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Axiomatic characterizations of Ptolemaic and chordal graphs [PDF]
Opuscula Mathematica, 2023 The interval function and the induced path function are two well studied class of set functions of a connected graph having interesting properties and applications to convexity, metric graph theory. Both these functions can be framed as special instances
Manoj Changat +2 more
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Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs [PDF]
Algorithmica, 2020 We study algorithmic properties of the graph class CHORDAL-ke\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
F. Fomin, P. Golovach
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Semipaired Domination in Some Subclasses of Chordal Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 A dominating set $D$ of a graph $G$ without isolated vertices is called semipaired dominating set if $D$ can be partitioned into $2$-element subsets such that the vertices in each set are at distance at most $2$. The semipaired domination number, denoted
Michael A. Henning +2 more
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