Characterization by forbidden induced subgraphs of some subclasses of chordal graphs

Q2 Mathematics
Sérgio H. Nogueira , Vinicius F. dos Santos
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引用次数: 0

Abstract

Chordal graphs are the graphs in which every cycle of length at least four has a chord. A set S is a vertex separator for vertices a and b if the removal of S of the graph separates a and b into distinct connected components. A graph G is chordal if and only if every minimal vertex separator is a clique. We study subclasses of chordal graphs defined by restrictions imposed on the intersections of its minimal separator cliques. Our goal is to characterize them by forbidden induced subgraphs. Some of these classes have already been studied such as chordal graphs in which two minimal separators have no empty intersection if and only if they are equal. Those graphs are known as strictly chordal graphs and they were first introduced as block duplicate graphs by Golumbic and Peled [Golumbic, M. C. and Peled, U. N., Block duplicate graphs and a hierarchy of chordal graphs, Discrete Applied Mathematics, 124 (2002) 67–71], they were also considered in [Kennedy, W., “Strictly chordal graphs and phylogenetic roots”, Master Thesis, University of Alberta, 2005] and [De Caria, P. and Gutiérrez, M., On basic chordal graphs and some of its subclasses, Discrete Applied Mathematics, 210 (2016) 261–276], showing that strictly chordal graphs are exactly the (gem, dart)-free graphs.

弦图若干子类的禁止诱导子图的刻画
弦图是指每个长度至少为4的循环都有一个弦的图。如果图中S的移除将A和b分离为不同的连通分量,则集合S是顶点A和b的顶点分隔符。图G是弦的当且仅当每个最小顶点分隔符都是团。研究了弦图的子类,这些子类是由弦图的最小分隔团的交点所限定的。我们的目标是用禁止诱导子图来描述它们。其中一些类已经被研究过了,比如弦图,其中两个最小分隔符当且仅当相等时没有空交集。这些图被称为严格弦图,它们最初是由Golumbic和Peled作为块复制图引入的[Golumbic, m.c.和Peled,联合国,块复制图和弦图的层次,离散应用数学,124(2002)67-71],它们也被考虑在[Kennedy, W.,“严格弦图和系统发生根”,硕士论文,阿尔伯塔大学,2005]和[De Caria, P.和guti录影带,M.,关于基本弦图及其一些子类,离散应用数学,210(2016)261-276],表明严格弦图正是无(gem, dart)图。
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来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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