English

The robber strikes back

Combinatorics 2013-08-14 v1 Discrete Mathematics

Abstract

We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum number of cops needed to capture a robber on a graph GG, written cc(G)cc(G). We give bounds on cc(G)cc(G) in terms of the cop number of GG in the classes of bipartite graphs and diameter two, K1,mK_{1,m}-free graphs.

Keywords

Cite

@article{arxiv.1308.2843,
  title  = {The robber strikes back},
  author = {Anthony Bonato and Stephen Finbow and Przemyslaw Gordinowicz and Ali Haidar and William B. Kinnersley and Dieter Mitsche and Pawel Pralat and Ladislav Stacho},
  journal= {arXiv preprint arXiv:1308.2843},
  year   = {2013}
}
R2 v1 2026-06-22T01:08:36.994Z