Original Articles

The mixed irredundant Ramsey numbers t(3, 7) = 18 and t(3, 8) = 22

Published in: Quaestiones Mathematicae
Volume 37 , issue 4 , 2014 , pages: 571–589

DOI: 10.2989/16073606.2014.894691

Author(s): A.P. Burger Department of Logistics, South Africa , J.H. Hattingh Department of Mathematics, United States of America , J.H. van Vuuren Department of Logistics, South Africa

Keywords: Irredundance , Ramsey number , Irredundance , Ramsey number

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Abstract

The mixed irredundant Ramsey number t(m, n) is the smallest natural number t such that if the edges of the complete graph K_t on t vertices are arbitrarily bi-coloured using the colours blue and red, then necessarily either the subgraph induced by the blue edges has an irredundant set of cardinality m or the subgraph induced by the red edges has an independent set of cardinality n (or both). Previously it was known that 18 ≤ t(3, 7) ≤ 22 and 18 ≤ t(3, 8) ≤ 28. In this paper we prove that t(3, 7) = 18 and t(3, 8) = 22.

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