ORTH and Ingrid
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چکیده
For graphs G and H the Ramsey number r(G, W) is defined to be the least number p such that every 2-coloring (say green and red) of the edges of the complete graph KP contains either a subgraph G with all its edges green, or a subgraph M with all its edges red. The diagonal Ramsey numbers r(G, G) = r(G) for G = K,, are of particular interest. The values r(&) = 6, and r(&) = 18 are well known, but r(K5) is still unknown; all that is presently known is th:at 42 < r( KS) s 55. If the numbers r(G) are considered only for graphs G with at most five vertices, then for all G with at most six edges the Ramsey numbers are listed in [ 11. For nine edges only one graph, KS e, exists, and t( KS e) = 22 recently was proved in [3]. For ten edges r(K5) remains open. Thus it remains to consider (except for KS) only graphs with seven or eight edges (Figs. 1 and 2). It will be seen that the corresponding Ramsey numbers are:
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تاریخ انتشار 2001