Abstract
AbstractPetruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex $$x \in V(G)$$
x
∈
V
(
G
)
there exists a colour c appearing an odd number of times in its neighbourhood N(x). Petruševski and Škrekovski proved that for any planar graph G there is an odd colouring using at most 9 colours and, together with Caro, showed that 8 colours are enough for a significant family of planar graphs. We show that 8 colours suffice for all planar graphs.
Funder
Engineering and Physical Sciences Research Council
Cambridge Commonwealth, European and International Trust
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Theoretical Computer Science
Cited by
3 articles.
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