Small on-line Ramsey numbers---a new approach

Authors

  • Pawel Pralat Ryerson University
  • Przemyslaw Gordinowicz Lodz University of Technology

DOI:

https://doi.org/10.11575/cdm.v13i2.62731

Keywords:

on-line Ramsey numbers

Abstract

In this note, we revisit the problem of calculating small on-line Ramsey numbers R(G,H). A new approach is proposed that reduces the running time of the algorithm determining that R(K_3,K_4)=17 by a factor of at least 2*10^6 comparing to the previously used approach. Using high performance computing networks, we determined that R(K_4,K_4) <= 26, R(K_3,K_5) < 25, and that R(K_3,K_3,K_3) <= 20 for a natural generalization to three colours. All graphs on 3 or 4 vertices are investigated as well, including non-symmetric cases.

Author Biography

Pawel Pralat, Ryerson University

Associate Professor, Department of Mathematics

Assistant Director of Industry Liaison
The Fields Institute for Research in Mathematical Sciences

References

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12. P. Prałat, A note on small on-line Ramsey numbers for paths and their generalization, Australasian Journal of Combinatorics 40 (2008), 27-36.

13. P. Prałat, R(3; 4) = 17, Electronic Journal of Combinatorics 15 (2008), #R67, 13pp.

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16. D. B. West, Introduction to graph theory, 2nd ed., Prentice Hall, 2001.

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Published

2018-12-31

Issue

Vol. 13 No. 2 (2018)

Section

Articles

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