A remark on star-C4 and wheel-C4 Ramsey numbers
| Main Authors: | Zhang, Yanbo; Department of Mathematics, Nanjing University, Nanjing, P.R. China, Broersma, Hajo; Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands, Chen, Yaojun; Department of Mathematics, Nanjing University, Nanjing, P.R. China |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2014
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/73 http://www.ejgta.org/index.php/ejgta/article/view/73/22 |
Daftar Isi:
- Given two graphs G1 and G2, the Ramsey number R(G1;G2)is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n+1 and Sn a star of order n. In this paper, it is shown that R(Wn;C4) = R(Sn+1;C4) for n ≥ 6. Based on this result and Parsons' results on R(Sn+1;C4), we establish the best possible general upper bound for R(Wn;C4) and determine some exact values for R(Wn;C4).