On the minimum order of 4-lazy cops-win graphs

Sim, Kai An and Tan, Ta Sheng and Wong, Kok Bin (2018) On the minimum order of 4-lazy cops-win graphs. Bulletin of the Korean Mathematical Society, 55 (6). pp. 1667-1690. ISSN 1015-8634

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Official URL: http://pdf.medrang.co.kr/kms01/BKMS/55/BKMS-55-6-1...

Abstract

We consider the minimum order of a graph G with a given lazy cop number c L (G). Sullivan, Townsend and Werzanski [7] showed that the minimum order of a connected graph with lazy cop number 3 is 9 and K 3 □K 3 is the unique graph on nine vertices which requires three lazy cops. They conjectured that for a graph G on n vertices with ∆(G) ≥ n − k 2 , c L (G) ≤ k. We proved that the conjecture is true for k = 4. Furthermore, we showed that the Petersen graph is the unique connected graph G on 10 vertices with ∆(G) ≤ 3 having lazy cop number 3 and the minimum order of a connected graph with lazy cop number 4 is 16.

Item Type: Article
Uncontrolled Keywords: Cops and Robbers; vertex-pursuit games; minimum order
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Science > Institute of Mathematical Sciences
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 12 Mar 2019 02:03
Last Modified: 12 Mar 2019 02:03
URI: http://eprints.um.edu.my/id/eprint/20660

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