CO-irredundant Ramsey numbers
Date
1998
Authors
Simmons, Jill
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Abstract
Given a graph G = (V, E), a subset of vertices S is CO-irredundant if for any vertex v in S, the closed neighbourhood of v is not contained in the union of the open neighbourhoods of the vertices of S - {v}. The CO-irredundant Ramsey number t(l, m) is the least value of n such that any n-vertex graph G either has a CO-irredundant vertex subset of at least m vertices, or its complement G has a CO-irredundant vertex subset of at least l vertices. The existence of these number is guaranteed by Ramsey's theorem. We prove that t(4, 5 ) = 8, t(4, 6) = 11, t(4, 7) = 14, t(3 , m) = m, and t(3, 3, m) = 2m - 1 or 2m - 2 for m odd or even respectively. We also prove that t(n 1, , nk) = R(Fi , , Fk) where n, E {3 , 4} and Fi = P3(C4) if na = e(4). Bounds will be given for t(5, 5).