The harmonious chromatic number of almost all trees

TY - JOUR

T1 - The harmonious chromatic number of almost all trees

AU - Edwards, Keith

PY - 1995

Y1 - 1995

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 of colours in such a colouring. For any positive integer m, let Q(m) be the least positive integer k such that (*) S: m. We show that for almost all unlabelled, unrooted trees T, h(T) = Q(m), where m is the number of edges of T. Copyright © Cambridge University Press 1995

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 of colours in such a colouring. For any positive integer m, let Q(m) be the least positive integer k such that (*) S: m. We show that for almost all unlabelled, unrooted trees T, h(T) = Q(m), where m is the number of edges of T. Copyright © Cambridge University Press 1995

U2 - 10.1017/S0963548300001462

DO - 10.1017/S0963548300001462

M3 - Article

SN - 0963-5483

VL - 4

SP - 31

EP - 46

JO - Combinatorics, Probability and Computing

JF - Combinatorics, Probability and Computing

IS - 1

ER -