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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

We construct smallest known trivalent graphs for girths 16 and 18. One construction uses voltage graphs, and the other coset enumeration techniques for group presentations.

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)