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This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short overview of past results, and then by presenting several general constructions establishing new lower bounds for many diagonal and off-diagonal multicolor Ramsey numbers. In particular, we improve several lower bounds for
A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v +e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and(More)
For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K3. For integers m and n, let [m, n] denote the set {i | m ≤ i ≤ n}. A set S of integers is called sum-free if i, j ∈ S implies i + j ∈ S, where we allow i = j. The Schur function S(k) is defined for all positive integers as the maximum n such that [1, n](More)