Mathematics > Combinatorics
[Submitted on 4 Aug 2018 (v1), last revised 17 Aug 2019 (this version, v4)]
Title:Regular behaviour of the maximal hypergraph chromatic number
View PDFAbstract:Let $m(n,r)$ denote the minimal number of edges in an $n$-uniform hypergraph which is not $r$-colorable. It is known that for a fixed $n$ one has \[ c_n r^n < m(n,r) < C_n r^n. \] We prove that for any fixed $n$ the sequence $a_r := m(n,r)/r^n$ has a limit, which was conjectured by Alon. We also prove the list colorings analogue of this statement.
Submission history
From: Danila Cherkashin [view email][v1] Sat, 4 Aug 2018 13:14:43 UTC (5 KB)
[v2] Mon, 17 Sep 2018 18:37:23 UTC (6 KB)
[v3] Thu, 11 Jul 2019 10:56:42 UTC (6 KB)
[v4] Sat, 17 Aug 2019 07:02:15 UTC (9 KB)
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