Amalgamations of almost regular edge-colourings of simple graphs
Journal of Combinatorial Theory Series A
A separator theorem for graphs with an excluded minor and its applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The harmonious coloring number of a graph
Discrete Mathematics - Special issue: advances in graph labelling
The complexity of harmonious colouring for trees
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
On the harmonious coloring of collections of graphs
Journal of Graph Theory
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Combinatorics, Probability and Computing
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A detachment of a graph $G$ is formed by splitting each vertex into one or more subvertices, and sharing the incident edges arbitrarily among the subvertices. In this paper we consider the question of whether a graph $H$ is a detachment of some complete graph $K_n$. When $H$ is large and restricted to belong to certain classes of graphs, for example bounded degree planar triangle-free graphs, we obtain necessary and sufficient conditions which give a complete characterization.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. The results on detachments of complete graphs give exact results on harmonious chromatic number for many classes of graphs, as well as algorithmic results.