弦图的约化团图

IF 1 3区数学 Q1 MATHEMATICS

European Journal of Combinatorics Pub Date : 2012-07-01 DOI:10.1016/j.ejc.2011.09.031

Michel Habib , Juraj Stacho

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引用次数: 26

摘要

我们从弦图允许树表示这一众所周知的事实出发，研究了弦图的性质。特别地，我们研究了降团图的结构，降团图是经典地捕获弦图的所有树表示的图。我们提出了一种基于两种操作的约简团图的新分解：边收缩和分割边的去除。基于这种分解，我们刻画了弦图中的星形集，并讨论了允许具有少量叶子的树表示的弦图。

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Reduced clique graphs of chordal graphs

We investigate the properties of chordal graphs that follow from the well-known fact that chordal graphs admit tree representations. In particular, we study the structure of reduced clique graphs which are graphs that canonically capture all tree representations of chordal graphs. We propose a novel decomposition of reduced clique graphs based on two operations: edge contraction and removal of the edges of a split. Based on this decomposition, we characterize asteroidal sets in chordal graphs, and discuss chordal graphs that admit a tree representation with a small number of leaves.

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来源期刊

European Journal of Combinatorics 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.