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arXiv · 1807.06285

Fractional chromatic number of a random subgraph

Bojan Mohar·Hehui Wu
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Abstract

It is well known that a random subgraph of the complete graph $K_n$ has chromatic number $Θ(n/\log n)$ w.h.p. Boris Bukh asked whether the same holds for a random subgraph of any $n$-chromatic graph, at least in expectation. In this paper it is shown that for every graph, whose fractional chromatic number is at least $n$, the fractional chromatic number of its random subgraph is at least $n/(8\log_2(4n))$ with probability more than $1-\frac{1}{2n}$. This gives the affirmative answer for a strengthening of Bukh's question for the fractional chromatic number.

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Bojan Mohar, Hehui Wu. 2018-07-17. Fractional chromatic number of a random subgraph. https://arxiv.org/abs/1807.06285

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