Homomorphisms from sparse graphs with large girth

Authors:
O. V. Borodin;S.-J. Kim;A. V. Kostochka;D. B. West
Affiliations:
Institute of Mathematics, 630090 Novosibirsk, Novosibirsk, Russia;Department of Mathematics, University of Illinois, Urbana, IL;Institute of Mathematics, 630090 Novosibirsk, Novosibirsk, Russia and Department of Mathematics, University of Illinois, Urbana, IL;Department of Mathematics, University of Illinois, Urbana, IL
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

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Abstract

We show that a planar graph with girth at least 20t - 2/3 has circular chromatic number at most 2 + 1/t, improving earlier results. This follows from a general result establishing homomorphisms into special targets for graphs with given girth and given maximum average degree. Other applications concern oriented chromatic number and homomorphisms into mixed graphs with colored edges.