Publication at Faculty of Mathematics and Physics |
2019
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 3/11 n. (C) 2019 Elsevier Ltd. All rights reserved.