Homomorphisms from sparse graphs with large girth

doi:10.1016/S0095-8956(03)00081-9

Journal of Combinatorial Theory, Series B

Volume 90, Issue 1, January 2004, Pages 147-159

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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.

Keywords

Graph coloring

Graph homomorphism

Planar graph

Circular coloring

Oriented coloring

Discharging

t-Nice graphs

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¹: Partially supported by Grants 99-01-00581 and 00-01-00916 of the Russian Foundation for Fundamental Research and the Dutch-Russian Grant NWO-047-008-006.

²: Partially supported by NSF Grant DMS-0099608 and by INTAS grant 97-1001.

³: Partially supported by NSA Grant MDA904-03-1-0037. The US grants supporting A.V. Kostochka and D.B. West require the disclaimer that any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the NSF or NSA.