O. V. Borodin, A. O. Ivanova, “An oriented $7$-colouring of planar graphs with girth at least $7$”, Sib. Èlektron. Mat. Izv., 2005, Volume 2,Pages 222

This article is cited in 10 papers

Research papers

An oriented $7$-colouring of planar graphs with girth at least $7$

O. V. Borodin^a, A. O. Ivanova^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Yakutsk State University

Abstract: An oriented $k$-colouring of digraph $H$ is an oriented homomorphism of $H$ into a $k$-vertex tournament. We prove that every orientation of a plane graph with girth at least $7$ has an oriented $7$-colouring.

UDC: 519.172.2

MSC: 05C15

Received October 4, 2005, published November 3, 2005