The paper studies the existence of (n + 1)-cliques in k-connected graphs. It is proved that, in a k-connected graph G, such a clique exists, provided that the following conditions are fulfilled: (1) the vertices of every n-clique of G belong to a k-cutset; (2) the removal of certain pairs each of which consists of a vertex and an edge decreases the connectivity of the graph G by 2.
展开▼
