Work

A proof of the 3/5-conjecture in the domination game

Year: 2024

Type: article

Abstract: The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph 𝐺 . A vertex is said to be dominated if it has been selected or is adjacent to a selected vertex. Each selected vertex must strictly increase the number of dominated vertices at the time of its selection, and the game ends once every vertex in 𝐺 is dominated. Dominator aims to keep the game as short as possible, while Staller tries to achieve the opposite. In this article, we prove that for any graph 𝐺 on 𝑛 vertices, Dominator has a strategy to end the game in at most 3 ⁢ 𝑛 / 5 moves, which was conjectured by Kinnersley, West and Zamani.

Source: European Journal of Combinatorics

DOI: 10.1016/j.ejc.2024.104034

Author: Leo Versteegen

Institution: University of Cambridge

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,000

Funder: Trinity College, University of Cambridge