منابع مشابه
Note on the game chromatic index of trees
We study edge coloring games defining the so-called game chromatic index of a graph. It has been reported that the game chromatic index of trees with maximum degree ∆ = 3 is at most ∆ + 1. We show that the same holds true in case ∆ ≥ 6, which would leave only the cases ∆ = 4 and ∆ = 5 open.
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We prove that the game chromatic index of n-wheels is n for n ≥ 6. © 2010 Elsevier B.V. All rights reserved.
متن کاملThe irregular chromatic index of trees
A graph G is locally irregular if adjacent vertices of G have distinct degrees. An edge colouring of G is locally irregular if each of its colours induces a locally irregular subgraph of G. The irregular chromatic index of G refers to the least number of colours used by a locally irregular edge colouring of G (if any). We propose a linear-time algorithm for determining the irregular chromatic i...
متن کاملGame chromatic index of k-degenerate graphs
We consider the following edge coloring game on a graph G. Given t distinct colors, two players Alice and Bob, with Alice moving ®rst, alternately select an uncolored edge e of G and assign it a color different from the colors of edges adjacent to e. Bob wins if, at any stage of the game, there is an uncolored edge adjacent to colored edges in all t colors; otherwise Alice wins. Note that when ...
متن کاملGame chromatic index of graphs with given restrictions on degrees
Given a graph G and an integer k, two players alternatively color the edges of G using k colors so that adjacent edges get different colors. The game chromatic index χg(G) is the minimum k for which the first player has a strategy that ensures that all edges of G get colored. The trivial bounds are ∆(G) ≤ χg(G) ≤ 2∆(G)−1, where ∆(G) denote the maximal degree of G. Lam, Shiu, and Xu and, indepen...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2004
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2002.10.002