The capture time of a planar graph

Photchchara Pisantechakool () and Xuehou Tan
Additional contact information
Photchchara Pisantechakool: Tokai University
Xuehou Tan: Tokai University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 4, No 1, 1103-1117

Abstract: Abstract This paper examines the capture time of a planar graph in a variant of the pursuit-evasion games, called cops and robbers game. Since any planar graph is 3-cop-win, we study the capture time of a planar graph G of n vertices using three cops, which is denoted by $$capt_3(G)$$ c a p t 3 ( G ) . We present a new capture strategy and show that $$capt_3(G) \le 2n$$ c a p t 3 ( G ) ≤ 2 n . This is the first result on $$capt_3(G)$$ c a p t 3 ( G ) .

Keywords: Cops and robbers game; Capture time; Guarded shortest path; Robber territory (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-017-0173-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:36:y:2018:i:4:d:10.1007_s10878-017-0173-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-017-0173-6

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().