Beveridge, Andrew, Bohman, Tom, Frieze, Alan and Pikhurko, Oleg (2008) Game chromatic index of graphs with given restrictions on degrees. Theoretical Computer Science, Vol.407 (No.1-3). pp. 242-249. doi:10.1016/j.tcs.2008.05.026

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Abstract

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 indexView the MathML source 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 View the MathML source, where Δ(G) denotes the maximal degree of G. Lam, Shiu, and Xu and, independently, Bartnicki and Grytczuk asked whether there is a constant C such that View the MathML source for every graph G. We show that the answer is in the negative by constructing graphs G such that View the MathML source and Δ(G)→∞. On the other hand, we show that for every μ>0 there is ε>0 such that for any graph G with Δ(G)≥(1/2+μ)v(G), we have View the MathML source, where v(G) denotes the number of vertices of G.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Theoretical Computer Science
Publisher:	Elsevier Science BV
ISSN:	0304-3975
Official Date:	2008
Dates:	Date Event 2008 Published
Volume:	Vol.407
Number:	No.1-3
Number of Pages:	8
Page Range:	pp. 242-249
DOI:	10.1016/j.tcs.2008.05.026
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	NSF
Grant number:	DMS-0701183, CCR-0502793, DMS-0457512

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