Domination Game

2021 ◽  
pp. 9-46
Author(s):  
Boštjan Brešar ◽  
Michael A. Henning ◽  
Sandi Klavžar ◽  
Douglas F. Rall
Keyword(s):  
Domination Game

scholarly journals Domination game: extremal families for 3/5-conjecture for forests

2017 ◽  
Vol 37 (2) ◽  
pp. 369 ◽  
Author(s):  
Michael .A. Henning ◽  
Christian Löwenstein
Keyword(s):  
Domination Game

Total Domination Game

2021 ◽  
pp. 47-62
Author(s):  
Boštjan Brešar ◽  
Michael A. Henning ◽  
Sandi Klavžar ◽  
Douglas F. Rall
Keyword(s):  
Total Domination ◽  
Total Domination Game ◽  
Domination Game

scholarly journals Domination game: Extremal families of graphs for3/5-conjectures

2013 ◽  
Vol 161 (10-11) ◽  
pp. 1308-1316 ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Gašper Košmrlj ◽  
Douglas F. Rall
Keyword(s):  
Domination Game

scholarly journals The domination game played on unions of graphs

2015 ◽  
Vol 338 (1) ◽  
pp. 71-79 ◽  
Author(s):  
Paul Dorbec ◽  
Gašper Košmrlj ◽  
Gabriel Renault
Keyword(s):  
Domination Game

Effect of vertex-removal on game total domination numbers

2019 ◽  
Vol 13 (07) ◽  
pp. 2050129
Author(s):  
Karnchana Charoensitthichai ◽  
Chalermpong Worawannotai
Keyword(s):  
Domination Number ◽  
Total Domination ◽  
Total Domination Number ◽  
Connected Graphs ◽  
Isolated Vertex ◽  
Vertex Removal ◽  
Total Domination Game ◽  
Domination Game ◽  
Domination Numbers

The total domination game is played on a graph [Formula: see text] by two players, named Dominator and Staller. They alternately select vertices of [Formula: see text]; each chosen vertex totally dominates its neighbors. In this game, each chosen vertex must totally dominates at least one new vertex not totally dominated before. The game ends when all vertices in [Formula: see text] are totally dominated. Dominator’s goal is to finish the game as soon as possible, and Staller’s goal is to prolong it as much as possible. The game total domination number is the number of chosen vertices when both players play optimally, denoted by [Formula: see text] when Dominator starts the game and denoted by [Formula: see text] when Staller starts the game. In this paper, we show that for any graph [Formula: see text] and a vertex [Formula: see text], where [Formula: see text] has no isolated vertex, we have [Formula: see text] and [Formula: see text]. Moreover, all such differences can be realized by some connected graphs.

scholarly journals Progress towards the total domination game 34-conjecture

2016 ◽  
Vol 339 (11) ◽  
pp. 2620-2627 ◽  
Author(s):  
Michael A. Henning ◽  
Douglas F. Rall
Keyword(s):  
Total Domination ◽  
Total Domination Game ◽  
Domination Game

scholarly journals Domination game on paths and cycles

2017 ◽  
Vol 13 (1) ◽  
pp. 125-136 ◽  
Author(s):  
Gašper Košmrlj
Keyword(s):  
Domination Game

scholarly journals Domination game critical graphs

2015 ◽  
Vol 35 (4) ◽  
pp. 781 ◽  
Author(s):  
Csilla Bujtás ◽  
Sandi Klavžar ◽  
Gašper Košmrlj
Keyword(s):  
Critical Graphs ◽  
Domination Game

scholarly journals Guarded subgraphs and the domination game

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Gasper Košmrlj ◽  
Doug F. Rall
Keyword(s):  
Graph Theory ◽  
Domination Number ◽  
Metric Properties ◽  
International Audience ◽  
Game Domination Number ◽  
Domination Game

Graph Theory International audience We introduce the concept of guarded subgraph of a graph, which as a condition lies between convex and 2-isometric subgraphs and is not comparable to isometric subgraphs. Some basic metric properties of guarded subgraphs are obtained, and then this concept is applied to the domination game. In this game two players, Dominator and Staller, alternate choosing vertices of a graph, one at a time, such that each chosen vertex enlarges the set of vertices dominated so far. The aim of Dominator is that the graph is dominated in as few steps as possible, while the aim of Staller is just the opposite. The game domination number is the number of vertices chosen when Dominator starts the game and both players play optimally. The main result of this paper is that the game domination number of a graph is not smaller than the game domination number of any guarded subgraph. Several applications of this result are presented.

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