TY - JOUR

T1 - The harmonious chromatic number of bounded degree graphs

AU - Edwards, K.

N1 - Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 1997

Y1 - 1997

N2 - A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number ot colours in such a colouring. Let d be a fixed positive integer, and e > 0. We show that there is a natural number M such that if G is any graph with m = M edges and maximum degree at most d, then the harmonious chromatic number h(G) satisfies (2m) = h(G) = (1+e) (2m).

AB - A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number ot colours in such a colouring. Let d be a fixed positive integer, and e > 0. We show that there is a natural number M such that if G is any graph with m = M edges and maximum degree at most d, then the harmonious chromatic number h(G) satisfies (2m) = h(G) = (1+e) (2m).

UR - http://www.scopus.com/inward/record.url?scp=0031156405&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031156405

SN - 0024-6107

VL - 55

SP - 435

EP - 447

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -