Stephen Mellendorf

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We consider the following two problems. (1) Let t and n be positive integers with n ≥ t ≥ 2. Determine the maximum number of edges of a graph of order n that contains neither Kt nor Kt,t as a subgraph. (2) Let r, t and n be positive integers with n ≥ rt and t ≥ 2. Determine the maximum number of edges of a graph of order n that does not contain r disjoint(More)
We define the multicycle C m as a cycle on m vertices where each edge has multiplicity r. So C m can be decomposed into r Hamilton cycles. We provide a complete answer to the following question: for which positive integers m, n, r, s with m, n ≥ 3 can the Cartesian product of two multicycles C m × C n be decomposed into r + s Hamilton cycles? We find some(More)
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