Graphs with large chromatic number induce $3k$-cycles
Graphs with large chromatic number induce $3k$-cycles
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具有大色数的图会引发 $3k$ 循环
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Stéphan Thomassé
中科院分区：
文献类型：
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作者：
Marthe Bonamy;Pierre Charbit;Stéphan Thomassé
回答 Kalai 和 Meshulam 的问题，我们证明没有长度为 3k 的诱导环的图具有有界色数。这意味着更广泛的问题的第一个情况，即每个具有大色数的图都会归纳出一个图 H，使得 H 的独立复形的贝蒂数之和也很大。
Answering a question of Kalai and Meshulam, we prove that graphs without induced cycles of length 3k have bounded chromatic number. This implies the very first case of a much broader question asserting that every graph with large chromatic number induces a graph H such that the sum of the Betti numbers of the independence complex of H is also large.