Résumé
Let$K\_{[k,t]}$be the complete graph on$k$vertices from which a set of edges, induced by a clique of order$t$ , has been dropped. In this note we give two explicit upper bounds for$R(K\_{[k\_1,t\_1]},\dots, K\_{[k\_r,t\_r]})$(the smallest integer$n$such that for any$r$ -edge coloring of$K\_n$there always occurs a monochromatic$K\_{[k\_i,t\_i]}$for some$i$ ). Our first upper bound contains a classical one in the case when$k\_1=\cdots =k\_r$and$t\_i=1$for all$i$ . The second one is obtained by introducing a new edge coloring called$\chi\_r$ -colorings. We finally discuss a conjecture claiming, in particular, that our second upper bound improves the classical one in infinitely many cases.