Alspach, Brian; Gerson, Martin; Hahn, Gena; Hell, Pavol On sub-Ramsey numbers. (English) Zbl 0603.05031 Ars Comb. 22, 199-206 (1986). Given a graph G and a natural number k, the sub-Ramsey number sr(G,k) is the least integer m so that, if the complete graph on m vertices is edge colored in such a way that no color is used more than k times, then there is an isomorphic copy of G all of whose edges have distinct colors. The paper includes several proofs of the existence of sr(G,k) as well as some exact values and bounds for sr(G,k), in the case G is a complete graph. For example: Theorem: Let \(n\geq 4\) and \(k\geq 2\). Then, \[ k(n- 1)+1\leq sr(K_ n,k)\leq \{n(n-1)(n-2)(k-1)+3\}/4. \] Reviewer: J.E.Graver Cited in 6 Documents MSC: 05C55 Generalized Ramsey theory Keywords:sub-Ramsey number PDFBibTeX XMLCite \textit{B. Alspach} et al., Ars Comb. 22, 199--206 (1986; Zbl 0603.05031)