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For any two graphs F 1 and F 2 , the graph Ramsey number r(F 1 , F 2) is the smallest positive integer N with the property that every graph on at least N vertices contains F 1 or its complement contains F 2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. We determine r(θ n , K m) for m = 2, 3, 4 and n > m. More… (More)

For two positive integers r and s, G(n; r, s) denotes to the class of graphs on n vertices containing no r of s-edge disjoint cycles and f (n; r, s) = max{E(G) : G ∈ G(n; r, s)}. In this paper, for integers r ≥ 2 and k ≥ 1, we determine f (n; r, 2k + 1) and characterize the edge maximal members in G(n; r, 2k + 1).

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