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, Volume 32, Issue 3, pp 347–361 | Cite as

The Relaxed Edge-Coloring Game and k-Degenerate Graphs

  • Charles Dunn
  • David Morawski
  • Jennifer Firkins Nordstrom
Article

Abstract

The (r, d)-relaxed edge-coloring game is a two-player game using r colors played on the edge set of a graph G. We consider this game on forests and more generally, on k-degenerate graphs. If F is a forest with Δ(F)=Δ, then the first player, Alice, has a winning strategy for this game with r=Δ−j and d≥2j+2 for 0≤j≤Δ−1. This both improves and generalizes the result for trees in Dunn, C. (Discret. Math. 307, 1767–1775, 2007). More broadly, we generalize the main result in Dunn, C. (Discret. Math. 307, 1767–1775, 2007) by showing that if G is k-degenerate with Δ(G)=Δ and j∈[Δ+k−1], then there exists a function h(k,j) such that Alice has a winning strategy for this game with r=Δ+kj and dh(k,j).

Keywords

Competitive coloring k-degenerate graph Edge coloring 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Charles Dunn
    • 1
  • David Morawski
    • 2
  • Jennifer Firkins Nordstrom
    • 1
  1. 1.Linfield CollegeMcMinnvilleUSA
  2. 2.University of MinnesotaMinneapolisUSA

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