scholarly journals The relaxed game chromatic index of k-degenerate graphs

2007 ◽  
Vol 307 (14) ◽  
pp. 1767-1775 ◽  
Author(s):  
Charles Dunn
Keyword(s):  
Chromatic Index ◽  
Game Chromatic Index

scholarly journals The game chromatic index of wheels

2011 ◽  
Vol 159 (16) ◽  
pp. 1660-1665 ◽  
Author(s):  
Stephan Dominique Andres ◽  
Winfried Hochstättler ◽  
Christiane Schallück
Keyword(s):  
Chromatic Index ◽  
Game Chromatic Index

scholarly journals A New Upper Bound on the Game Chromatic Index of Graphs

10.37236/7451 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Ralph Keusch
Keyword(s):  
Computer Science ◽  
Upper Bound ◽  
Maximum Degree ◽  
Theoretical Computer Science ◽  
Chromatic Index ◽  
Theoretical Computer ◽  
Player Game ◽  
Delta G ◽  
Game Chromatic Index

We study the two-player game where Maker and Breaker alternately color the edges of a given graph $G$ with $k$ colors such that adjacent edges never get the same color. Maker's goal is to play such that at the end of the game, all edges are colored. Vice-versa, Breaker wins as soon as there is an uncolored edge where every color is blocked. The game chromatic index $\chi'_g(G)$ denotes the smallest $k$ for which Maker has a winning strategy.The trivial bounds $\Delta(G) \le \chi_g'(G) \le 2\Delta(G)-1$ hold for every graph $G$, where $\Delta(G)$ is the maximum degree of $G$. Beveridge, Bohman, Frieze, and Pikhurko conjectured that there exists a constant $c>0$ such that for any graph $G$ it holds $\chi'_g(G) \le (2-c)\Delta(G)$ [Theoretical Computer Science 2008], and verified the statement for all $\delta>0$ and all graphs with $\Delta(G) \ge (\frac12+\delta)|V(G)|$. In this paper, we show that $\chi'_g(G) \le (2-c)\Delta(G)$ is true for all graphs $G$ with $\Delta(G) \ge C \log |V(G)|$. In addition, we consider a biased version of the game where Breaker is allowed to color $b$ edges per turn and give bounds on the number of colors needed for Maker to win this biased game.

scholarly journals Note on the game chromatic index of trees

2004 ◽  
Vol 313 (3) ◽  
pp. 371-376 ◽  
Author(s):  
Peter L. Erdös ◽  
Ulrich Faigle ◽  
Winfried Hochstättler ◽  
Walter Kern
Keyword(s):  
Chromatic Index ◽  
Game Chromatic Index

A Note on the Game Chromatic Index of Graphs

2008 ◽  
Vol 24 (2) ◽  
pp. 67-70 ◽  
Author(s):  
Tomasz Bartnicki ◽  
Jarosław Grytczuk
Keyword(s):  
Chromatic Index ◽  
Game Chromatic Index
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