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Induced Subgraphs of Graphs With Large Chromatic Number. X. Holes of Specific Residue
Combinatorica ( IF 1.1 ) Pub Date : 2019-10-02 , DOI: 10.1007/s00493-019-3804-y
Alex Scott , Paul Seymour

A large body of research in graph theory concerns the induced subgraphs of graphs with large chromatic number, and especially which induced cycles must occur. In this paper, we unify and substantially extend results from a number of previous papers, showing that, for every positive integer k, every graph with large chromatic number contains either a large complete subgraph or induced cycles of all lengths modulo k. As an application, we prove two conjectures of Kalai and Meshulam from the 1990's connecting the chromatic number of a graph with the homology of its independence complex.

中文翻译:

大色数图的诱导子图。X. 特定残留物的孔

图论中的大量研究涉及具有大色数的图的诱导子图,尤其是必须发生的诱导循环。在本文中,我们统一并大幅扩展了之前许多论文的结果,表明对于每个正整数 k,每个具有大色数的图都包含一个大的完整子图或所有长度模 k 的诱导循环。作为应用,我们证明了 1990 年代 Kalai 和 Meshulam 的两个猜想,将图的色数与其独立复数的同源性联系起来。
更新日期:2019-10-02
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