The eternal dominating set problem for interval graphs
Mart\'in Rinemberg, Francisco J. Soulignac
TL;DR
This paper establishes a key equivalence between eternal domination and clique-connected cover numbers in interval graphs and provides a linear algorithm for solving the eternal dominating set problem.
Contribution
It proves the equivalence of two domination parameters in interval graphs and introduces a linear-time algorithm for the eternal dominating set problem.
Findings
Eternal domination and clique-connected cover numbers are equal in interval graphs.
A linear algorithm for the eternal dominating set problem is developed.
The results simplify solving the eternal dominating set problem in interval graphs.
Abstract
We prove that, in games in which all the guards move at the same turn, the eternal domination and the clique-connected cover numbers coincide for interval graphs. A linear algorithm for the eternal dominating set problem is obtained as a by-product.
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