On certain subgraphs of a complete transitively directed graph

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-go...

On Subgraphs of the Complete Bipartite Graph

G(n) denotes a graph of n vertices and G(n) denotes its complementary graph. In a complete graph every two distinct vertices are joined by an edge. Let C k (G(n)) denote the number of complete subgraphs of k vertices contained in G(n). Recently it was proved [1] that for every k 2 (n) (1) min C (G (n)) + Ck(G(n)) < k k, , ! 2 2 where the minimum is over all graphs G(n). It seems likely that (1)...

Random Subgraphs of Certain Graph Powers

On the number of complete subgraphs of a graph II

Generalizing some results of P . ERnbs and sonic of L . MosER and J. W. MOON we give lower bounds *on the number of complete p-graphs K p of,graphs in terms of the numbers of vertices and edges. Further, for some values of n and E we give a complete characterization of the extremal graphs, i.e. the graphs S of n vertices and E edges having minimum number of K,'s. Our results contain the proof o...

On the number of complete subgraphs contained in certain graphs

We count the number of complete graphs of order 4 contained in certain graphs.