Induced subgraphs of graphs with large chromatic number. I. Odd holes
نویسندگان
چکیده
An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyárfás made the conjecture that for all t there exists n such that every graph with no Kt subgraph and no odd hole is n-colourable. We prove this conjecture.
منابع مشابه
Induced subgraphs of graphs with large chromatic number. VIII. Long odd holes
We prove a conjecture of András Gyárfás, that for all κ, `, every graph with clique number at most κ and sufficiently large chromatic number has an odd hole of length at least `.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 121 شماره
صفحات -
تاریخ انتشار 2016