THE TRIPARTITE RAMSEY NUMBERS r\(_t\)(C\(_4\); 2) AND r\(_t\)(C\(_4\); 3)

Authors

  • S. Buada Nakhon Sawan Rajabhat University - Department of Science
  • D. Samana King Mongkut's Institute of Technology Ladkrabang - Department of Mathematics
  • V. Longani Chiang Mai University - Department of Mathematics

Keywords:

tripartite Ramsey numbers, bipartite Ramsey numbers, Ramsey numbers, tripartite graphs, bipartite graphs

Abstract

The k-colored tripartite Ramsey numbers rt(G; k) is the smallest positive integer n such that any k-coloring of lines of a complete tripartite graph Kn,n,n there always exists a monochromatic subgraph isomorphic to G.  When G is C4 it is known, but unpublished in a journal, that rt(C4; 2) = 3.  In this paper we simplify the proof of rt(C4; 2) = 3 and show the new result that rt(C4; 3) = 7.

Cover of n°33 Italian Journal of Pure and Applied Mathematics

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Published

2014-12-29

How to Cite

Buada, S., Samana, D., & Longani, V. (2014). THE TRIPARTITE RAMSEY NUMBERS r\(_t\)(C\(_4\); 2) AND r\(_t\)(C\(_4\); 3). Italian Journal of Pure and Applied Mathematics, 33, 383–400. Retrieved from https://journals.uniurb.it/index.php/ijpam/article/view/6276

Issue

N°33 - December 2014

Section

Articoli - Forum Editrice

License

Copyright (c) 2014 S. Buada, D. Samana, V. Longani

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

L'opera è pubblicata sotto  Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)