Effect of predomination and vertex removal on the game total domination number of a graph

DOI10.1016/j.dam.2018.09.011zbMath1406.05070arXiv1802.03637OpenAlexW2963588429WikidataQ129046488 ScholiaQ129046488MaRDI QIDQ1730237

Vesna Iršič

Publication date: 11 March 2019

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

Full work available at URL: https://arxiv.org/abs/1802.03637

zbMATH Keywords

critical graphstotal domination gamegame total domination number

Mathematics Subject Classification ID

2-person games (91A05) Games involving graphs (91A43) Structural characterization of families of graphs (05C75) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Games on graphs (graph-theoretic aspects) (05C57)

Related Items (11)

Predominating a vertex in the connected domination game ⋮ Uniform length dominating sequence graphs ⋮ Perfect graphs for domination games ⋮ General upper bound on the game domination number ⋮ Total connected domination game ⋮ An Introduction to Game Domination in Graphs ⋮ Game total domination for cyclic bipartite graphs ⋮ Effect of vertex-removal on game total domination numbers ⋮ Fractional domination game ⋮ Connected domination game: Predomination, Staller-start game, and lexicographic products ⋮ On Rall's 1/2-conjecture on the domination game

Cites Work

• Game total domination for cycles and paths
• Characterisation of forests with trivial game domination numbers
• The domination game played on unions of graphs
• Total version of the domination game
• Domination game critical graphs
• Further progress on the heredity of the game domination number
• The 4/5 upper bound on the game total domination number
• Domination game: effect of edge- and vertex-removal
• Trees with equal total domination and game total domination numbers
• The game total domination problem is log-complete in PSPACE
• Progress towards the total domination game \(\frac{3}{4}\)-conjecture
• Transversal Game on Hypergraphs and the $\frac{3}{4}$-Conjecture on the Total Domination Game
• Domination Game and an Imagination Strategy
• Domination Game: A proof of the $3/5$-Conjecture for Graphs with Minimum Degree at Least Two
• Extremal Problems for Game Domination Number

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