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

Pawel Pralat, Przemyslaw Gordinowicz

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.


Keywords


on-line Ramsey numbers

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

DOI (PDF): https://doi.org/10.11575/cdm.v13i2.62731.g46828

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Contributions to Discrete Mathematics. ISSN: 1715-0868