Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Five Cycles are Highly Ramsey Infinite

  • Siggers, Mark (Department of Mathematics, Kyungpook National University)
  • Received : 2010.09.02
  • Accepted : 2011.03.07
  • Published : 2012.03.23
Download PDF
⟨ Previous Next ⟩

Abstract

In a previous paper, the author proved that all odd cycles, except five cycles, are highly Ramsey-infinite. In this paper, we fill in the missing case, and show that five cycles are highly Ramsey-infinite.

Keywords

References

  1. B. Bollobas, J. Donadelli, Y. Kohayakawa, R.H. Schelp, Ramsey minimal graphs, J. of the Brazilian Computer Society, 7(3)(2002), 27-37.
  2. S. Burr, J. Nesetril,V. Rodl, On the use of senders in generalized Ramsey theory for graphs, Discrete Math., 54(1)(1985), 1-13. https://doi.org/10.1016/0012-365X(85)90057-3
  3. R. Faudree, Ramsey minimal graphs for forests, Ars Combin., 31(1991), 117-124.
  4. J. Nesetril, V. Rodl, Partitions of vertices, Comment. Math. Univ. Carolinae, 17(1)(1976), 85-95.
  5. J. Nesetril, V. Rodl, The structure of critical Ramsey graphs, Acta Math. Acad. Sci. Hungar., 32(3-4)(1978), 295-300. https://doi.org/10.1007/BF01902367
  6. V. Rodl, A. Rucinski, Threshold functions for Ramsey properties, J. Amer. Math. Soc., 8(4)(1995), 917-942. https://doi.org/10.1090/S0894-0347-1995-1276825-6
  7. V. Rodl, M. Siggers, On Ramsey Minimal Graphs, SIAM J. Discrete Math., 22(2)(2008), 467-488. https://doi.org/10.1137/050647116
  8. M. Siggers, On Highly Ramsey Infinite Graphs, J. Graph Theory, 59(2)(2008), 97-114. https://doi.org/10.1002/jgt.20324

Cited by

  1. Non-bipartite pairs of -connected graphs are highly Ramsey-infinite vol.36, 2014, https://doi.org/10.1016/j.ejc.2013.06.001