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Independence complexes of chordal graphs

机译:弦图的独立复合体

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摘要

We show that the independence complex I (G) of an arbitrary chordal graph G is either contractible or is homotopy equivalent to the finite wedge of spheres of dimension at least the domination number of G minus 1. Also it is shown that every finite wedge of spheres (as well as a singleton) is realized as the homotopy type of the independence complex of a chordal graph. A combinatorial consequence is a verification of a conjecture due to Aharoni et?al. [2, Conjecture 2.4] for chordal graphs.
机译:我们表明,任意弦图G的独立复数I(G)是可收缩的,或者是等价性,等于尺寸球的有限楔形至少等于G的控制数减去1。球体(以及单例)被实现为弦图独立性复合体的同伦类型。组合结果是对Aharoni等人的猜想的验证。 [2,猜想2.4]用于弦图。

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