List rankings and on-line list rankings of graphs
نویسندگان
چکیده
منابع مشابه
On-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...
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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 کاملRankings of Directed Graphs
A ranking of a graph is a coloring of the vertex set with positive integers such that on every path connecting two vertices of the same color there is a vertex of larger color. We consider the directed variant of this problem, where the above condition is imposed only on those paths in which all edges are oriented in the same direction. We show that the ranking number of a directed tree is boun...
متن کاملRankings of Graphs
A vertex (edge) coloring φ : V → {1, 2, . . . , t} (φ′ : E → {1, 2, . . . , t}) of a graph G = (V,E) is a vertex (edge) t-ranking if, for any two vertices (edges) of the same color, every path between them contains a vertex (edge) of larger color. The vertex ranking number χr(G) (edge ranking number χ′ r (G)) is the smallest value of t such that G has a vertex (edge) t-ranking. In this paper we...
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.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.12.014