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Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs [PDF]
Discrete Applied Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ryuhei Uehara
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Connected graph searching in chordal graphs
Discrete Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nicolas Nisse
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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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On chordal phylogeny graphs [PDF]
Discrete Applied Mathematics, 2021 An acyclic digraph each vertex of which has indegree at most $i$ and outdegree at most $j$ is called an $(i, j)$ digraph for some positive integers $i$ and $j$. Lee {\it et al.} (2017) studied the phylogeny graphs of $(2, 2)$ digraphs and gave sufficient conditions and necessary conditions for $(2, 2)$ digraphs having chordal phylogeny graphs.
Soogang Eoh, Suh-Ryung Kim
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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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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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Hyperbolicity and Chordality of a Graph [PDF]
The Electronic Journal of Combinatorics, 2011 Let $G$ be a connected graph with the usual shortest-path metric $d$. The graph $G$ is $\delta$-hyperbolic provided for any vertices $x,y,u,v$ in it, the two larger of the three sums $d(u,v)+d(x,y),d(u,x)+d(v,y)$ and $d(u,y)+d(v,x)$ differ by at most $2\delta.$ The graph $G$ is $k$-chordal provided it has no induced cycle of length greater than $k ...
Yaokun Wu, Chengpeng Zhang
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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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