Asymptotically the List Colouring Constants Are 1
نویسندگان
چکیده
منابع مشابه
Asymptotically the List Colouring Constants Are 1
In this paper we prove the following result about vertex list colourings, which shows that a conjecture of the first author (1999, J. Graph Theory 31, 149–153) is asymptotically correct. Let G be a graph with the sets of lists SðvÞ; satisfying that for every vertex jSðvÞj 1⁄4 ð1þ oð1ÞÞd and for each colour c 2 SðvÞ; the number of neighbours of v that have c in their list is at most d : Then the...
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A natural generalization of graph colouring involves taking colours from a metric space and insisting that the endpoints of an edge receive colours separated by a minimum distance dictated by properties of the edge. In the q-backbone colouring problem, these minimum distances are either q or 1, depending on whether or not the edge is in the backbone. In this paper we consider the list version o...
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We consider the two-player game defined as follows. Let (G,L) be a graph G with a list assignment L on its vertices. The two players, Alice and Bob, play alternately on G, Alice having the first move. Alice’s goal is to provide an L-colouring of G and Bob’s goal is to prevent her from doing so. A move consists in choosing an uncoloured vertex v and assigning it a colour from the set L(v). Adjac...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2002
ISSN: 0095-8956
DOI: 10.1006/jctb.2002.2110