منابع مشابه
On-line List Colouring of Random Graphs
In this paper, the on-line list colouring of binomial random graphs G (n, p) is studied. We show that the on-line choice number of G (n, p) is asymptotically almost surely asymptotic to the chromatic number of G (n, p), provided that the average degree d = p(n − 1) tends to infinity faster than (log logn)(logn)n. For sparser graphs, we are slightly less successful; we show that if d ≥ (logn) fo...
متن کاملOn-Line List Colouring of Graphs
This paper studies on-line list colouring of graphs. It is proved that the online choice number of a graph G on n vertices is at most χ(G) ln n + 1, and the on-line b-choice number of G is at most eχ(G)−1 e−1 (b − 1 + lnn) + b. Suppose G is a graph with a given χ(G)-colouring of G. Then for any (χ(G) ln n + 1)-assignment L of G, we give a polynomial time algorithm which constructs an L-colourin...
متن کاملList Colouring Big Graphs On-Line
In this paper, we investigate the problem of graph list colouring in the on-line setting. We provide several results on paintability of graphs in the model introduced by Schauz [13] and Zhu [19]. We prove that the on-line version of Ohba’s conjecture is true in the class of planar graphs. We also consider several alternate on-line list colouring models.
متن کاملOn-Line List Colouring of Complete Multipartite Graphs
The Ohba Conjecture says that every graph G with |V (G)| ≤ 2χ(G) + 1 is chromatic choosable. This paper studies an on-line version of Ohba Conjecture. We prove that unlike the off-line case, for k ≥ 3, the complete multipartite graph K2?(k−1),3 is not on-line chromatic-choosable. Based on this result, the on-line version of Ohba Conjecture is modified as follows: Every graph G with |V (G)| ≤ 2χ...
متن کاملGame List Colouring of Graphs
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: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/5003