On the minimum order of 4-lazy cops-win graphs
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...
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Korean Mathematical Society
2018
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my.um.eprints.206602019-03-12T02:03:05Z http://eprints.um.edu.my/20660/ On the minimum order of 4-lazy cops-win graphs Sim, Kai An Tan, Ta Sheng Wong, Kok Bin Q Science (General) QA Mathematics 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. Korean Mathematical Society 2018 Article PeerReviewed 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 http://pdf.medrang.co.kr/kms01/BKMS/55/BKMS-55-6-1667-1690.pdf doi:10.4134/BKMS.b170948 |
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Q Science (General) QA Mathematics Sim, Kai An Tan, Ta Sheng Wong, Kok Bin On the minimum order of 4-lazy cops-win graphs |
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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. |
| format |
Article |
| author |
Sim, Kai An Tan, Ta Sheng Wong, Kok Bin |
| author_facet |
Sim, Kai An Tan, Ta Sheng Wong, Kok Bin |
| author_sort |
Sim, Kai An |
| title |
On the minimum order of 4-lazy cops-win graphs |
| title_short |
On the minimum order of 4-lazy cops-win graphs |
| title_full |
On the minimum order of 4-lazy cops-win graphs |
| title_fullStr |
On the minimum order of 4-lazy cops-win graphs |
| title_full_unstemmed |
On the minimum order of 4-lazy cops-win graphs |
| title_sort |
on the minimum order of 4-lazy cops-win graphs |
| publisher |
Korean Mathematical Society |
| publishDate |
2018 |
| url |
http://eprints.um.edu.my/20660/ http://pdf.medrang.co.kr/kms01/BKMS/55/BKMS-55-6-1667-1690.pdf |
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