The eternal dominating set problem for interval graphs

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.



There are no comments yet.


page 1

page 2

page 3


Balanced Independent and Dominating Sets on Colored Interval Graphs

We study two new versions of independent and dominating set problems on ...

On Streaming Algorithms for the Steiner Cycle and Path Cover Problem on Interval Graphs and Falling Platforms in Video Games

We introduce a simplified model for platform game levels with falling pl...

Parameterized algorithms for locating-dominating sets

A locating-dominating set D of a graph G is a dominating set of G where ...

Total 2-domination of proper interval graphs

A set of vertices W of a graph G is a total k-dominating set when every ...

On combinatorial optimization for dominating sets (literature survey, new models)

The paper focuses on some versions of connected dominating set problems:...

Characterizing subclasses of cover-incomparability graphs by forbidden subposets

In this paper we demonstrate that several theorems from Bres and Bres3 d...

Eternal Domination and Clique Covering

We study the relationship between the eternal domination number of a gra...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.


  • Booth and Lueker [1976] K. S. Booth and G. S. Lueker. Testing for the consecutive ones property, interval graphs, and graph planarity using -tree algorithms. J. Comput. System Sci., 13(3):335–379, 1976. doi: 10.1016/S0022-0000(76)80045-1.
  • Braga et al. [2015] A. Braga, C. C. de Souza, and O. Lee. The eternal dominating set problem for proper interval graphs. Inform. Process. Lett., 115(6-8):582–587, 2015. doi: 10.1016/j.ipl.2015.02.004.
  • Burger et al. [2004] A. P. Burger, E. J. Cockayne, W. R. Gründlingh, C. M. Mynhardt, J. H. van Vuuren, and W. Winterbach. Infinite order domination in graphs. J. Combin. Math. Combin. Comput., 50:179–194, 2004.
  • Goddard et al. [2005] W. Goddard, S. M. Hedetniemi, and S. T. Hedetniemi. Eternal security in graphs. J. Combin. Math. Combin. Comput., 52:169–180, 2005.
  • Klostermeyer and MacGillivray [2009] W. F. Klostermeyer and G. MacGillivray. Eternal dominating sets in graphs. J. Combin. Math. Combin. Comput., 68:97–111, 2009.
  • Klostermeyer and Mynhardt [2016] W. F. Klostermeyer and C. M. Mynhardt. Protecting a graph with mobile guards. Appl. Anal. Discrete Math., 10(1):1–29, 2016. doi: 10.2298/AADM151109021K.