THE MIXED IRREDUNDANT RAMSEY NUMBERS t(3,7)=18 AND t(3,8)=22

摘要

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.