Lower Bounds of Some Small Bipartite Ramsey Numbers br(K2,2;Kn,n)

Abstract

For bipartite graphs G₁,G₂, the bipartite Ramsey number br(G₁,G₂) is the smallest integer b such that any subgraph G of the complete bipartite graph K_b,_b,either G contains
a copy of G₁ or its complement relative to K_b._b contains a copy of G₂ . We obtained lower bounds of br(K₂,₂;K_n,n) for . for 6< n < 10

Keywords: Bipartite Ramsey numbers, lower bounds, graphs.

*Corresponding author: E-mail: numai_6060@hotmail.com

How to Cite

Citation Format

Adsawatithisakul, N. ., Summart*, W. ., Samana, D. ., & Samana, D. . (2018). Lower Bounds of Some Small Bipartite Ramsey Numbers br(K2,2;Kn,n). CURRENT APPLIED SCIENCE AND TECHNOLOGY, 154-161.

References

Beineke, L.W. and Schwenk, A.J., 1975. On a bipartite form of the Ramsey problem, Proc. 5th British Combin. Conf. 1975, Congressus Numer, XV, 17-22.
Longani, V., 2002. Some Bipartite Ramsey Numbers, Southeast Asian Bulletin of Mathematics, 26(4), 583-592.
Hattingh, J.H. and Henning, M.A., 1998. Bipartite Ramsey theory, Utilitas Math, 53, 217-230.
Carnielli, W.A. and Camelo, E.L.M., 2000. and bipartite Ramsey numebers, Discrete Mathematics, 223, 83-92.
Goddard, W., Henning, M.A. and Oellermann, O.R., 2000. Bipartite Ramsey Numbers and Zarankiewicz Numbers, Discrete Mathematics, 29, 85-95.

Author Information

Nitiphoom Adsawatithisakul

Department of Mathematics, Faculty of Science and Technology, Nakhonratchasima Rajabhat University, Nakhonratchasima, Thailand

Waraporn Summart*

General Education Affair, Thonburi University, Thailand

Decha Samana

Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, Thailand

Decha Samana

Centre of Excellence in Mathematics, Commission of Higher Education, Bangkok, Thailand

About this Article

Journal

Vol. 17 No. 2 (2017)

Type of Manuscript

Original Research Article

Keywords

Bipartite Ramsey numbers, lower bounds, graphs.

Published

5 January 2018

Lower Bounds of Some Small Bipartite Ramsey Numbers Br(K2,2;Kn,n)

Abstract

How to Cite

References

Author Information

Nitiphoom Adsawatithisakul

Waraporn Summart*

Decha Samana

Decha Samana

About this Article

Journal

Type of Manuscript

Keywords

Published

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