Edge Folkman numbers Fe(G1, G2; k) can be viewed as a generalization of more commonly studied Ramsey numbers. Fe(G1, G2; k) is defined as the smallest order of any Kk -free graph F such that any red-blue coloring of the edges of F contains either a red G1 or a blue G2. In this note, first we discuss edge Folkman numbers involving graphs Js = Ks − e, including the results Fe(J3, Kn; n + 1) = 2n − 1, Fe(J3, Jn; n) = 2n − 1, and Fe(J3, Jn; n + 1) = 2n − 3. Our modification of computational methods used previously in the study of classical Folkman numbers is applied to obtain upper bounds on Fe(J4, J4; k) for all k > 4.
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Kaufmann, Jenny M.; Wickus, Henry J.; and Radziszowski, Stanislaw, "On Some Edge Folkman Numbers Small and Large" (2019). Involve, a Journal of Mathematics, 12 (), 813--822. Accessed from
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