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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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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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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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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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Componentwise linearity of ideals arising from graphs [PDF]
Le Matematiche, 2008 Let G be a simple undirected graph on n vertices.
Veronica Crispin, Eric Emtander
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The leafage of a chordal graph
Discussiones Mathematicae Graph Theory, 1998 The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes.
Lin, In-Jen +2 more
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Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A graph $G$ is equitably $k$-choosable if, for any given $k$-uniform list assignment $L$, $G$ is $L$-colorable and each color appears on at most $\lceil\frac{|V(G)|}{k}\rceil$ vertices.
Aijun Dong, Jianliang Wu
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The Hadwiger number, chordal graphs and -perfection
AKCE International Journal of Graphs and Combinatorics, 2017 A graph is chordal if every induced cycle has three vertices. The Hadwiger number is the order of the largest complete minor of a graph. We characterize the chordal graphs in terms of the Hadwiger number and we also characterize the families of graphs ...
Christian Rubio-Montiel
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How is a Chordal Graph like a Supersolvable Binary Matroid? [PDF]
Discrete Mathematics, 2002 Raul Cordovil +2 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
semanticscholar +1 more source