Strong Chromatic Index of Graphs With Maximum Degree Four
نویسندگان
چکیده
منابع مشابه
The chromatic index of graphs with large maximum degree
By Vizing’s theorem, the chromatic index x’(G) of a simple graph G satisfies d(G) Li 1 V(G)1 J + ir, where r is the number of vertices of maximum degree. A graph G is critical if G is Class 2 and x’(H) < x’(G) for all prop...
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We conjecture that any graphG with treewidth k and maximum degree ∆(G) ≥ k + √ k satisfies χ′(G) = ∆(G). In support of the conjecture we prove its fractional version.
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The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching. In this paper, we present bounds for the strong chromatic index of three different products of graphs in terms of the strong chromatic index of each factor. For the Cartesian product of paths, cycles or complete graphs, we derive sharper ...
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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: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7016