CO-irredundant Ramsey numbers

dc.contributor.author	Simmons, Jill	en_US
dc.date.accessioned	2024-08-15T18:23:05Z
dc.date.available	2024-08-15T18:23:05Z
dc.date.copyright	1998	en_US
dc.date.issued	1998
dc.degree.department	Department of Mathematics and Statistics
dc.degree.level	Master of Science M.Sc.	en
dc.description.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).
dc.format.extent	56 pages
dc.identifier.uri	https://hdl.handle.net/1828/19695
dc.rights	Available to the World Wide Web	en_US
dc.title	CO-irredundant Ramsey numbers	en_US
dc.type	Thesis	en_US

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