ON COMPLETE TOPOLOGICAL SUBGRAPHS OF CERTAIN GRAPHS

Let G he a graph . We say that G contains a complete k-gon if there are !c vertices of G any two of which are connected by an edge, we say that it contains a complete topological k-gon if it contains k vertices any two of which are connected by paths no two of which have a common vertex (except endpoints) . Following G . DIRAC we will denote complete k-gons by -k = and complete topological k-gons by G(k, 1) denotes a graph of k vertices and 1 edges