The Complexity of Harmonious Colouring for Trees
نویسندگان
چکیده
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. It was shown by Hopcroft and Krishnamoorthy (1983) that the problem of determining the harmonious chromatic number of a graph is NP-hard. We show here that the problem remains hard even when restricted to trees.
منابع مشابه
On Harmonious Colouring of Trees
Let G be a simple graph and (G) denote the maximum degree of G. A harmonious colouring of 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. In this paper it is shown that if T is a tree of order n and (T ) n2 , then there exists a harmonious colouring of T w...
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 57 شماره
صفحات -
تاریخ انتشار 1995