List Edge and List Total Colourings of Multigraphs
نویسندگان
چکیده
منابع مشابه
List Edge and List Total Colourings of Multigraphs
This paper exploits the remarkable new method of Galvin (J. Combin. Theory Ser. B 63 (1995), 153 158), who proved that the list edge chromatic number /$list(G) of a bipartite multigraph G equals its edge chromatic number /$(G). It is now proved here that if every edge e=uw of a bipartite multigraph G is assigned a list of at least max[d(u), d(w)] colours, then G can be edge-coloured with each e...
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The List Edge Colouring Conjecture asserts that, given any multigraph G with chromatic index k and any set system fSe : e 2 E(G)g with each jSej = k, we can choose elements se 2 Se such that se 6 = sf whenever e and f are adjacent edges. Using a technique of Alon and Tarsi which involves the graph monomial Q fxu ? xv : uv 2 Eg of an oriented graph, we verify this conjecture for certain families...
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Erdős and Lovász conjectured in 1968 that for every graph G with χ(G) > ω(G) and any two integers s, t ≥ 2 with s+ t = χ(G)+1, there is a partition (S, T ) of the vertex set V (G) such that χ(G[S]) ≥ s and χ(G[T ]) ≥ t. Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for line graphs of multigraphs.
متن کاملList colourings of planar graphs
Let G = (V,E) be a graph, let f : V (G)→ N, and let k ≥ 0 be an integer. A list-assignment L of G is a function that assigns to each vertex v of G a set (list) L(v) of colors: usually each color is a positive integer. We say that L is an f -assignment if |L(v)| = f(v) for all v ∈ V , and a k-assignment if |L(v)| = k for all v ∈ V . A coloring ofG is a function φ that assigns a color to each ver...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1997
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1780