A note on planar 5-list colouring

Non-extendability at distance 4

Z. Tuza, M. Voigt

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

An L-list colouring of a graph G is a proper vertex colouring in which every vertex v gets a colour from a prescribed list L(v) of allowed colours. Albertson has posed the following problem: Suppose G is a planar graph and each vertex of G has been assigned a list of five colours. Let W C V(G) such that the distance between any two vertices of W is at least d (=4). Can any list colouring of W be extended to a list colouring of G ? We give a construction satisfying the assumptions for d = 4 where the required extension is not possible. As an even stronger property, in our example one can assign lists L(v) to the vertices of G with |L(t')|=3 for v£ W and |I(i>)| = 5 otherwise, such that an Z,-list colouring is not possible. The existence of such graphs is in sharp contrast with Thomassen's theorem stating that a list colouring is always possible if the vertices of 3-element lists belong to the same face of G (and the other lists have 5 colours each).

Original language English 169-172 4 Discrete Mathematics 251 1-3 Published - May 28 2002

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List Coloring
Coloring
Color
Vertex Coloring
Graph in graph theory
Vertex of a graph
Planar graph
Assign
Face
Theorem

Keywords

• Distance
• Graph
• List colouring
• Planar

ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Theoretical Computer Science

Cite this

In: Discrete Mathematics, Vol. 251, No. 1-3, 28.05.2002, p. 169-172.

Research output: Contribution to journalArticle

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KW - Distance

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