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arXiv · 1802.04179

Planar graphs without cycles of length 4 or 5 are (11:3)-colorable

Zdeněk Dvořák·Xiaolan Hu
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Abstract

A graph G is (a:b)-colorable if there exists an assignment of b-element subsets of {1,...,a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We show that every planar graph without cycles of length 4 or 5 is (11:3)-colorable, a weakening of recently disproved Steinberg's conjecture. In particular, each such graph with n vertices has an independent set of size at least 3n/11.

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Zdeněk Dvořák, Xiaolan Hu. 2019-07-14. Planar graphs without cycles of length 4 or 5 are (11:3)-colorable. https://arxiv.org/abs/1802.04179

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