Work

Progress towards the 1/2-Conjecture for the domination game

Year: 2024

Type: article

Abstract: The domination game is played on a graph G by two players, Dominator and Staller, who alternate in selecting vertices until each vertex in the graph G is contained in the closed neighbourhood of the set of selected vertices. Dominator’s aim is to reach this state in as few moves as possible, whereas Staller wants the game to last as long as possible. In this paper, we prove that if G has n vertices and minimum degree at least 2, then Dominator has a strategy to finish the domination game on G within 10n/17+1/17 moves, thus making progress towards a conjecture by Bujtás, Iršič and Klavžar.

Source: Discrete Applied Mathematics

DOI: 10.1016/j.dam.2024.03.001

Authors: Julien Portier, 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: $2,860

Funders: Cambridge Trust, Engineering and Physical Sciences Research Council, Trinity College, University of Cambridge