Gallai-like characterization of strong cocomparability graphs

IF 0.9 3区 数学 Q2 MATHEMATICS
Jing Huang
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引用次数: 0

Abstract

Strong cocomparability graphs are the reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01 , 10 $01,10$ . Strong cocomparability graphs form a subclass of cocomparability graphs (i.e., the complements of comparability graphs) and can be recognized in polynomial time. In his seminal paper, Gallai characterized cocomparability graphs in terms of a forbidden structure called asteroids. Gallai proved that cocomparability graphs are precisely those reflexive graphs which do not contain asteroids. In this paper, we give a characterization of strong cocomparability graphs which is analogous to Gallai's characterization for cocomparability graphs. We prove that strong cocomparability graphs are precisely those reflexive graphs which do not contain weak edge-asteroids (a weaker version of asteroids). Our characterization also leads to a polynomial time recognition algorithm for strong cocomparability graphs.

强可比性图的伽来样表征
强可比性图是反向图,其邻接矩阵可以通过行和列的同时排列来避免有行的子矩阵。强可比性图是可比性图(即可比性图的补充)的一个子类,可以在多项式时间内识别。在他的开创性论文中,加莱用一种叫做小行星的禁止结构来描述可比性图的特征。加莱证明,可比性图正是那些不包含小行星的反射图。在本文中,我们给出了强可比性图的一个特性描述,它类似于 Gallai 对可比性图的特性描述。我们证明,强可比性图恰恰是那些不包含弱边缘星状体(星状体的弱化版本)的反射图。我们的表征还带来了强可比性图的多项式时间识别算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Graph Theory
Journal of Graph Theory 数学-数学
CiteScore
1.60
自引率
22.20%
发文量
130
审稿时长
6-12 weeks
期刊介绍: The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .
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