Induced subgraphs of graphs with large chromatic number. X. Holes of specific residue
نویسندگان
چکیده
In an earlier paper, we proved (with Chudnovsky and Spirkl) that for all integers κ, ` ≥ 0, every graph with clique number at most κ and sufficiently large chromatic number has an odd hole of length at least `. Here we prove a strengthening, that for all integers κ, ` ≥ 0, every graph with clique number at most κ and sufficiently large chromatic number has a hole of every possible length modulo `.
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