ArticleOriginal scientific text

Title

Multicolor Ramsey numbers for some paths and cycles

Authors 1

Affiliations

  1. Institute of Mathematics, UMCS, Lublin, Poland

Abstract

We give the multicolor Ramsey number for some graphs with a path or a cycle in the given sequence, generalizing a results of Faudree and Schelp [4], and Dzido, Kubale and Piwakowski [2,3].

Keywords

cycle, path, Ramsey number

Bibliography

  1. S. Brandt, A sufficient condition for all short cycles, Discrete Appl. Math. 79 (1997) 63-66, doi: 10.1016/S0166-218X(97)00032-2.
  2. T. Dzido, Multicolor Ramsey numbers for paths and cycles, Discuss. Math. Graph. Theory 25 (2005) 57-65, doi: 10.7151/dmgt.1260.
  3. T. Dzido, M. Kubale and K. Piwakowski, On some Ramsey and Turán-type numbers for paths and cycles, Electr. J. Combin. 13 (2006) R55.
  4. R.J. Faudree and R.H. Schelp, Path Ramsey numbers in multicolorngs, J. Combin. Theory (B) 19 (1975) 150-160, doi: 10.1016/0095-8956(75)90080-5.
  5. A. Figaj and T. Łuczak, The Ramsey number for a triple of long even cycles, J. Combin. Theory (B) 97 (2007) 584-596, doi: 10.1016/j.jctb.2006.09.001.
  6. Y. Kohayakawa, M. Simonovits and J. Skokan, The 3-colored Ramsey numbers of odd cycles, Electr. Notes Discrete Math. 19 (2005) 397-402, doi: 10.1016/j.endm.2005.05.053.
  7. D.R. Woodall, Maximal circuits of graphs I, Acta Math. Acad. Sci. Hungar. 28 (1976) 77-80, doi: 10.1007/BF01902497.
Pages:
209-218
Main language of publication
English
Received
2007-12-13
Accepted
2008-07-04
Published
2009
Exact and natural sciences