Generalized Ramsey Numbers Involving Subdivision Graphs , and Related Problems in Graph Theory
نویسنده
چکیده
Let G l and G 2 be (simple) graphs. The Ramsey*number r(Gl ,G 2) is the smallest integer n such that if one colors the complete graph Kn in two colors I and II, then either color I contains G 1 as a subgraph or color II contains G 2. The systematic study of r(Gl ,G2) was initiated by F. Harary, although there were a few previous scattered results of We also note here that notation not defined follows Harary [ 6 ]. Chvátal [ 3] proved that if Tn is any tree on n vertices, then r(Tn ,K£) = (£-1)(n-1) + 1 Trivially, then, if Gn is a connected graph on n points, we have r(Gn ,Kt) > (Z-1)(n-1) + 1. It appears to be a general principle that if such a graph is sufficiently "sparse", equality holds. With this in mind, call a connected graph Gn on n points 1-good if
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