Results 21 to 30 of about 2,481 (263)
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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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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Polynomial kernels for edge modification problems towards block and strictly chordal graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe consider edge modification problems towards block and strictly chordal graphs, where one is given an undirected graph $G = (V,E)$ and an integer $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a block graph or
Maël Dumas +3 more
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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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Minimal toughness in special graph classes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Let $t$ be a positive real number. A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components, and all graphs are considered 0-tough. The toughness of a graph is the largest $t$ for which
Gyula Y. Katona, Kitti Varga
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Generating Chordal Graphs Included in Given Graphs [PDF]
, 2006 A chordal graph is a graph which contains no chordless cycle of at least four edges as an induced subgraph. The class of chordal graphs contains many famous graph classes such as trees, interval graphs, and split graphs, and is also a subclass of perfect
KIYOMI, Masashi, UNO, Takeaki
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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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Linear-time counting algorithms for independent sets in chordal graphs [PDF]
, 2005 We study some counting and enumeration problems for chordal graphs, especially concerning independent sets. We first provide the following efficient algorithms for a chordal graph: (1) a linear-time algorithm for counting the number of independent sets; (
Ryuhei Uehara +5 more
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Algorithmic Aspects of Secure Connected Domination in Graphs
Discussiones Mathematicae Graph Theory, 2021 Let G = (V, E) be a simple, undirected and connected graph. A connected dominating set S ⊆ V is a secure connected dominating set of G, if for each u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E and the set (S \ {v}) ∪ {u} is a connected dominating ...
Kumar Jakkepalli Pavan +1 more
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Counting the number of independent sets in chordal graphs [PDF]
, 2008 We study some counting and enumeration problems for chordal graphs, especially concerning independent sets. We first provide the following efficient algorithms for a chordal graph: (1) a linear-time algorithm for counting the number of independent sets; (
Uno, Takeaki +2 more
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