Clique-relaxed graph coloring

Dunn, Charles; Nordstrom, Jennifer Firkins; Naymie, Cassandra; Pitney, Erin; Sehorn, William; Suer, Charlie

doi:10.2140/involve.2011.4.127

Cited by 3 publications

(5 citation statements)

References 11 publications

(9 reference statements)

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“…The above result is a generalization of a result in [6] where the authors show that at most 4 colors are needed for Alice to have a winning strategy on any given forest. Next we generalize a result from a previous REU [2] in which the authors found that the 2-clique-relaxed game chromatic number of an outerplanar graph is at most 4.…”

Section: Theorem 32 [1]supporting

confidence: 61%

“…Recall that every outerplanar graph is a partial 2-tree. The above result is hence a generalization of the result in [2] where the authors showed that for any outerplanar graph G, χ…”

Section: Theorem 32 [1]supporting

confidence: 60%

“…Thus, for any partial k-tree, Alice can win the k-clique-relaxed game using only 4 colors. This theorem generalizes to all chordal graphs the result in [2] where the authors showed that for any outerplanar graph G, χ…”

mentioning

confidence: 65%

“…Furthermore, we focus on the game as it is played on chordal graphs and partial k-trees. We extend results from [6] and [2] by specifically looking at the k-clique-relaxed coloring game as played on partial k-trees.…”

Section: Introductionmentioning

confidence: 88%

“…In this paper we investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color α is legal for a vertex if said vertex has no neighbors colored α.…”

Section: Introductionmentioning

confidence: 99%

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Clique-Relaxed Competitive Graph Coloring

Alexis¹,

Shurbert²,

Dunn³

et al. 2014

Preprint

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Section: Theorem 32 [1]supporting

confidence: 61%

“…Recall that every outerplanar graph is a partial 2-tree. The above result is hence a generalization of the result in [2] where the authors showed that for any outerplanar graph G, χ…”

Section: Theorem 32 [1]supporting

confidence: 60%

mentioning

confidence: 65%

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Clique-Relaxed Competitive Graph Coloring

Alexis¹,

Shurbert²,

Dunn³

et al. 2014

Preprint

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Introduction to Competitive Graph Coloring

Dunn

Larsen

Nordstrom

2017

Foundations for Undergraduate Research in Mathematics

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The game chromatic number of trees and forests

Dunn

Larsen

Lindke

et al. 2015

Discrete Mathematics &Amp; Theoretical Computer Science

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International audience While the game chromatic number of a forest is known to be at most 4, no simple criteria are known for determining the game chromatic number of a forest. We first state necessary and sufficient conditions for forests with game chromatic number 2 and then investigate the differences between forests with game chromatic number 3 and 4. In doing so, we present a minimal example of a forest with game chromatic number 4, criteria for determining in polynomial time the game chromatic number of a forest without vertices of degree 3, and an example of a forest with maximum degree 3 and game chromatic number 4. This gives partial progress on the open question of the computational complexity of the game chromatic number of a forest.

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Clique-relaxed graph coloring

Cited by 3 publications

References 11 publications

Clique-Relaxed Competitive Graph Coloring

Clique-Relaxed Competitive Graph Coloring

Introduction to Competitive Graph Coloring

The game chromatic number of trees and forests

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