منابع مشابه
The incidence game chromatic number
We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For kdegenerate graphs with maximum degree ∆, the upper bound 2∆ + 4k − 2 for the incidence game chromatic number is given. If ∆ ≥ 5k, we improve this bound to the value 2∆ + 3k − 1. We also determine the exact incidence game chromatic number of...
متن کاملThe incidence game chromatic number of (a, d)-decomposable graphs
The incidence coloring game has been introduced in [S.D. Andres, The incidence game chromatic number, Discrete Appl. Math. 157 (2009), 1980– 1987] as a variation of the ordinary coloring game. The incidence game chromatic number ιg(G) of a graph G is the minimum number of colors for which Alice has a winning strategy when playing the incidence coloring game on G. In [C. Charpentier and É. Sopen...
متن کاملGame chromatic number of graphs
y Abstract We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particular, since a planar graph has acyclic chromatic number at most 5, we conclude that the g...
متن کاملThe game chromatic number of graphs
Suppose G = (V, E) is a graph. The game chromatic number of G is defined through a two-person game: the colouring game. Given a graph G and a set C of colours, Alice and Bob, with Alice playing first, take turns in playing the game. Each play by either player consists of colouring an uncoloured vertex of G with a colour from C. Both players need to respect the rule that no adjacent vertices sho...
متن کاملThe game chromatic number of random graphs
Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of G are colored. The game chromatic number χg(G) is the minimum k for which the first player has a winning strategy. In this paper we analyze the asymptotic behavior of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2007.10.021