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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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Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs [PDF]
Logical Methods in Computer Science, 2019 We show that the class of chordal claw-free graphs admits LREC$_=$-definable canonization. LREC$_=$ is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion.
Berit Grußien
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Discrete Mathematics & Theoretical Computer Science, 2019 Slimness of a graph measures the local deviation of its metric from a tree metric. In a graph $G=(V,E)$, a geodesic triangle $\bigtriangleup(x,y,z)$ with $x, y, z\in V$ is the union $P(x,y) \cup P(x,z) \cup P(y,z)$ of three shortest paths connecting ...
Feodor F. Dragan, Abdulhakeem Mohammed
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Decycling a graph by the removal of a matching: new algorithmic and structural aspects in some classes of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 A graph $G$ is {\em matching-decyclable} if it has a matching $M$ such that $G-M$ is acyclic. Deciding whether $G$ is matching-decyclable is an NP-complete problem even if $G$ is 2-connected, planar, and subcubic.
Fábio Protti, Uéverton S. Souza
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The Geodetic Hull Number is Hard for Chordal Graphs [PDF]
Electron. Notes Discret. Math., 2017 We show the hardness of the geodetic hull number for chordal ...
Bessy, Stéphane +3 more
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Counting and Sampling Labeled Chordal Graphs in Polynomial Time [PDF]
Embedded Systems and Applications, 2023 We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on $n$ vertices. Our algorithm solves a more general problem: given $n$ and $\omega$ as input, it computes the number of $\omega$-colorable labeled ...
Úrsula Hébert-Johnson +2 more
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Transitivity on subclasses of chordal graphs [PDF]
International Conference on Algorithms and Discrete Applied Mathematics, 2022 Let $G=(V, E)$ be a graph, where $V$ and $E$ are the vertex and edge sets, respectively. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \textit{dominates} $B$ if every vertex of $B$ is adjacent to at least one vertex of $A$ in $G$.
S. Paul, Kamal Santra
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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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Heroes in orientations of chordal graphs [PDF]
SIAM Journal on Discrete Mathematics, 2022 We characterize all digraphs H such that orientations of chordal graphs with no induced copy of H have bounded dichromatic number.
Pierre Aboulker +2 more
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Chordal graphs, higher independence and vertex decomposable complexes [PDF]
International journal of algebra and computation, 2021 Given a simple undirected graph $G$ there is a simplicial complex $\mathrm{Ind}(G)$, called the independence complex, whose faces correspond to the independent sets of $G$.
F. M. Abdelmalek +4 more
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