Results 11 to 20 of about 428,321 (154)
Choice Numbers of Chordal, Chordless, and Some Non-Chordal Graphs
MathematicsWe prove that chordal graphs are chromatic-choosable and present a decomposition theorem to help estimate the choice numbers for certain classes of chordless and non-chordal graphs.
Julian Allagan +3 more
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Well-partitioned chordal graphs [PDF]
, 2022 We introduce a new subclass of chordal graphs that generalizes the class of split graphs, which we call well-partitioned chordal graphs. A connected graph G is a well-partitioned chordal graph if there exist a partition P of the vertex set of G into ...
Lima, Paloma T. +8 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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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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Independent sets of maximum weight in apple-free graphs [PDF]
, 2010 We present the first polynomial-time algorithm to solve the maximum weight independent set problem for apple-free graphs, which is a common generalization of several important classes where the problem can be solved efficiently, such as claw-free graphs,
Lozin, Vadim V. +2 more
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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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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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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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自余弱弦图(On self-complementary weakly chordal graphs)
Zhejiang Daxue xuebao. Lixue ban, 2010 The class of self-complementary (sc) weakly chordal graphs is studied, which is a generalization of self-complementary chordal graphs, lower and upper bounds for the number of two-pairs in sc weakly chordal graphs have been obtained.
MERAJUDDIN() +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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