On the P-4-components of graphs

Raschle T.; Simon K.

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On the P-4-components of graphs

机译：关于图的P-4分量

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Two edges are called P-4-adjacent if they belong to the same P-4 (chordless path on four vertices). P-4-components, in our terminology, are the equivalence classes of the transitive closure of the P-4-adjacency relation. In this paper, new results on the structure of P-4-components are obtained. On the one hand, these results allow us to improve the complexity of orienting P-4-comparability graphs and of recognizing P-4-indifference graphs from O(n(5)) and O(n(6)) to O(m(2)). On the other hand, by combining the modular decomposition with the substitution of P-4-components, a new unique tree representation for arbitrary graphs is derived which generalizes the homogeneous decomposition introduced by Jamison and Olariu (SIAM J. Discrete Math. 8 (1995) 448-463). (C) 2000 Elsevier Science B.V. All rights reserved. [References: 21]

机译：如果两个边属于同一P-4（四个顶点上的无弦路径），则它们称为P-4-相邻。在我们的术语中，P-4-成分是P-4-邻接关系的传递闭合的等价类。在本文中，获得了有关P-4-组分结构的新结果。一方面，这些结果使我们能够改善定向P-4-可比图和识别从O（n（5））和O（n（6））到O（m）的P-4-差图的复杂性（2））。另一方面，通过将模块化分解与P-4-组件的替换相结合，可以得出任意图的新的唯一树表示形式，它概括了Jamison和Olariu引入的齐次分解（SIAM J.Discrete Math.8（1995 ）448-463）。（C）2000 Elsevier Science B.V.保留所有权利。 [参考：21]

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《Discrete Applied Mathematics》 |2000年第3期|共21页
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Raschle T.; Simon K.;
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正文语种 eng
中图分类离散数学;
关键词
Perfectly orderable graphs; Brittle graphs;

机译：完全有序图;脆图;

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1. On the P-4-components of graphs [J] . Raschle T., Simon K. Discrete Applied Mathematics . 2000,第3期

机译：关于图的P-4分量
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On the P-4-components of graphs

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