Progress towards the total domination game \(\frac{3}{4}\)-conjecture

DOI10.1016/j.disc.2016.05.014zbMath1339.05255arXiv1512.02916OpenAlexW2288499534WikidataQ123320386 ScholiaQ123320386MaRDI QIDQ2629270

Douglas F. Rall, Michael A. Henning

Publication date: 5 July 2016

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

Full work available at URL: https://arxiv.org/abs/1512.02916

zbMATH Keywords

total domination gamegame total domination number3/4-conjecture

Mathematics Subject Classification ID

Hypergraphs (05C65) Games on graphs (graph-theoretic aspects) (05C57)

Related Items (19)

Trees with equal total domination and game total domination numbers ⋮ The game total domination problem is log-complete in PSPACE ⋮ On the game total domination number ⋮ General upper bound on the game domination number ⋮ Infinite families of circular and Möbius ladders that are total domination game critical ⋮ Unnamed Item ⋮ 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 ⋮ Bounds on the 2-domination number ⋮ Total connected domination game ⋮ The variety of domination games ⋮ Game total domination critical graphs ⋮ An Introduction to Game Domination in Graphs ⋮ Game total domination for cyclic bipartite graphs ⋮ Fractional domination game ⋮ The orthogonal colouring game ⋮ Connected domination game: Predomination, Staller-start game, and lexicographic products ⋮ Connected domination game played on Cartesian products

Cites Work

• The disjoint domination game
• Game total domination for cycles and paths
• The domination game played on unions of graphs
• Total version of the domination game
• Domination game critical graphs
• Domination game played on trees and spanning subgraphs
• Domination game: effect of edge- and vertex-removal
• Realizations of the game domination number
• Domination game: extremal families of graphs for \(3/5\)-conjectures
• Domination Game and an Imagination Strategy
• Domination Game: A proof of the $3/5$-Conjecture for Graphs with Minimum Degree at Least Two
• Total Domination in Graphs
• Extremal Problems for Game Domination Number

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