Results 1 to 10 of about 756 (218)
Edge erasures and chordal graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph.
Jared Culbertson +2 more
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The Neighborhood Polynomial of Chordal Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor.
Helena Bergold +2 more
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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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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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A Short Proof of the Size of Edge-Extremal Chordal Graphs
Journal of Mathematical Sciences and Modelling, 2022 [3] have recently determined the maximum number of edges of a chordal graph with a maximum degree less than $d$ and the matching number at most $\nu$ by exhibiting a family of chordal graphs achieving this bound. We provide simple proof of their result.
Mordechai Shalom
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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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Efficient (j, k)-Dominating Functions
Discussiones Mathematicae Graph Theory, 2023 For positive integers j and k, an efficient (j, k)-dominating function of a graph G = (V, E) is a function f : V → {0, 1, 2, . . ., j} such that the sum of function values in the closed neighbourhood of every vertex equals k. The relationship between the
Klostermeyer William F. +3 more
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On the End-Vertex Problem of Graph Searches [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 End vertices of graph searches can exhibit strong structural properties and are crucial for many graph algorithms. The problem of deciding whether a given vertex of a graph is an end-vertex of a particular search was first introduced by Corneil, K\"ohler
Jesse Beisegel +6 more
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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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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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