منابع مشابه
The Distance-t Chromatic Index of Graphs
We consider two graph colouring problems in which edges at distance at most t are given distinct colours, for some fixed positive integer t. We obtain two upper bounds for the distance-t chromatic index, the least number of colours necessary for such a colouring. One is a bound of (2− ε)∆t for graphs of maximum degree at most ∆, where ε is some absolute positive constant independent of t. The o...
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We show that there exist linear-time algorithms that compute the strong chromatic index of Halin graphs, of maximal outerplanar graphs and of distance-hereditary graphs.
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Suppose D is a subset of all positive integers Z. The distance graph G(Z; D) is the graph with vertex set Z and two vertices x; y are adjacent if jx ? yj 2 D. This paper studies the chromatic number of G(Z; D). We shall concentrate on the case that jDj = 3 and give a complete classiication of those D = fa; b; cg for which b is a multiple of a and (G(Z; D)) = 3.
متن کاملThe Strong Chromatic Index of Random Graphs
The strong chromatic index of a graph G, denoted by χs(G), is the minimum number of colors needed to color its edges so that each color class is an induced matching. In this paper we analyze the asymptotic behavior of this parameter in a random graph G(n, p), for two regions of the edge probability p = p(n). For the dense case, where p is a constant, 0 < p < 1, we prove that with high probabili...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2013
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548313000473