Indicated coloring game on Cartesian products of graphs

Brešar, Boštjan; Jakovac, Marko; Štesl, Daša

doi:10.1016/j.dam.2020.11.007

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…The minimum number of colors k for which Ann has a winning strategy on G, no matter how Ben plays, is called the indicated chromatic number of G, and denoted by χ i (G). The described game was introduced by Grzesik under the name the indicated coloring game [16] and has since gained much attention from other authors [6,21,23,24].…”

Section: Introductionmentioning

confidence: 99%

On game chromatic vertex-critical graphs

Jakovac¹,

Štesl²

2021

Preprint

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Several games that arise from graph coloring have been introduced and studied. Let ϕ denote a graph invariant that arises from such a game. If G is a graph and ϕ(G −, where χ g denotes the standard game chromatic number, χ i denotes the indicated game chromatic number and χ A ig , χ AB ig denote two versions of the independence game chromatic number. Since the game chromatic number ϕ(G − x) can either decrease or increase with respect to ϕ(G), we distinguish between lower, upper and mixed vertexcriticality. We show that for ϕ ∈ {χ g , χ A ig , χ AB ig } the difference ϕ(G)−ϕ(G−x), x ∈ V (G), can be arbitrarily large. A characterization of 2-ϕ-game-vertex-critical and (connected) 3ϕ-lower-game-vertex-critical graphs for all ϕ ∈ {χ g , χ i , χ A ig , χ AB ig } is given. It is shown that χ g -game-vertex-critical, χ A ig -game-vertex-critical and χ AB ig -game-vertex-critical graphs are not necessarily connected. However, it is also shown that χ i -lower-game-vertex-critical graphs are always connected.

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Section: Introductionmentioning

confidence: 99%

On game chromatic vertex-critical graphs

Jakovac¹,

Štesl²

2021

Preprint

Self Cite

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show abstract

“…Recently, there are many research studies about combinatorial game on graphs For example, the Maker-Breaker games (see [13,14,17,18]), the cop and robber games (see [4,22,32]) and the graph coloring games (see [3,5,7]).…”

Section: Combinatorial Game Theorymentioning

confidence: 99%

Graph grabbing games and toucher-isolator games

Boriboon¹

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In this research, we study the graph grabbing game and the Toucher-Isolator game. In the graph grabbing game, we partially confirm a conjecture of Seacrest and Seacrest which states that Alice wins the game on every weighted connected bipartite even graph. In the Toucher-Isolator game, we give a simple alternative proof of a result of Räty that determines the most suitable tree on n vertices for Toucher which answers a question of Dowden, Kang, Mikalački and Stojaković.

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On Game Chromatic Vertex-Critical Graphs

Jakovac

Štesl

2022

Bull. Malays. Math. Sci. Soc.

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Indicated coloring game on Cartesian products of graphs

Cited by 3 publications

References 17 publications

On game chromatic vertex-critical graphs

On game chromatic vertex-critical graphs

Graph grabbing games and toucher-isolator games

On Game Chromatic Vertex-Critical Graphs

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