then the set of edges containing a given vertex v ~ V(G) define a graph G v. The graphs {Gvl v ~ V(G)} are subsumed by G. Each subsumed graph Gv is a graph with vertex-set V(G) v. They can form theâ€¦ (More)

Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partition of the verticesâ€¦ (More)

Let k > 1 be an integer. Let Pâ€™ be any set with 1 VI > k. We denote by ( [) the set of all k-subsets of V. A k-hypergraph G consists of a set V(G) of oertices and a set E(G) c ( â€œâ€˜,â€œ)) of edges. Ifâ€¦ (More)

Vertices u and v in the graph G are said to be pseudo-similar if G US G v but no automorphism of G maps u onto v. It is shown that a known procedure for constructing finite graphs with pairs ofâ€¦ (More)

A k-hypergraph G consists of a vertex-set V(G) and an edge-xet E(G), a set of k-subsets of V(G). If XE V(G), the edges of the induced subgraph G[X] are those edges of G whose vertices are allâ€¦ (More)

Let G be a simple, undirected graph. A special network N, called a balanced network, is constructed from G such that maximum matchings and f-factors in G correspond to maximum flows in N. Aâ€¦ (More)