Domination Game: A proof of the $3/5$-Conjecture for Graphs with Minimum Degree at Least Two

DOI10.1137/140976935zbMath1329.05210OpenAlexW2232004157WikidataQ123260294 ScholiaQ123260294MaRDI QIDQ3462542

William B. Kinnersley, Michael A. Henning

Publication date: 15 January 2016

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1029&context=math_facpubs

zbMATH Keywords

dominationdomination gamegame domination number

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Vertex degrees (05C07) Games on graphs (graph-theoretic aspects) (05C57)

Related Items (35)

Trees with equal total domination and game total domination numbers ⋮ Game total domination for cycles and paths ⋮ Progress towards the total domination game \(\frac{3}{4}\)-conjecture ⋮ The 3/5-conjecture for weakly \(S(K_{1, 3})\)-free forests ⋮ Complexity of the game domination problem ⋮ Mycielskian of graphs with small game domination number ⋮ Paired-Domination Game Played in Graphs ⋮ Maker-breaker total domination game ⋮ Paired-domination game played on cycles ⋮ General upper bound on the game domination number ⋮ Bounds for the competition-independence game on trees ⋮ The matcher game played in graphs ⋮ The 4/5 upper bound on the game total domination number ⋮ Infinite families of circular and Möbius ladders that are total domination game critical ⋮ Unnamed Item ⋮ THE DOMINATION GAME ON SPLIT GRAPHS ⋮ Domination game and minimal edge cuts ⋮ Cutting lemma and union lemma for the domination game ⋮ Effect of predomination and vertex removal on the game total domination number of a graph ⋮ Domination game on uniform hypergraphs ⋮ On graphs with largest possible game domination number ⋮ The enclaveless competition game ⋮ How long can one bluff in the domination game? ⋮ Domination game: extremal families for the 3/5-conjecture for forests ⋮ The variety of domination games ⋮ Game total domination critical graphs ⋮ On domination game stable graphs and domination game edge-critical graphs ⋮ An Introduction to Game Domination in Graphs ⋮ Transversal Game on Hypergraphs and the $\frac{3}{4}$-Conjecture on the Total Domination Game ⋮ \( 1 / 2\)-conjectures on the domination game and claw-free graphs ⋮ Fractional domination game ⋮ My Favorite Domination Conjectures in Graph Theory Are Bounded ⋮ Connected domination game: Predomination, Staller-start game, and lexicographic products ⋮ Connected domination game ⋮ The domination game played on diameter 2 graphs

Cites Work

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