In this paper, we present the index-permutation (IP) graph model, and apply it to the systematic development of efficient hierarchical networks. We derive several classes of inter...
Let H be a fixed directed graph on h vertices, let G be a directed graph on n vertices and suppose that at least n2 edges have to be deleted from it to make it H-free. We show tha...
Let H be a fixed graph on h vertices. We say that a graph G is induced H-free if it does not contain any induced copy of H. Let G be a graph on n vertices and suppose that at leas...
In this paper, we consider smooth words over 2-letter alphabets {a, b}, where a, b are integers having same parity, with 0 < a < b. We show that all are recurrent and that t...
We localize and strengthen Katona’s idea of an edge-toughness to a local topological toughness. We disprove a conjecture of Katona concerning the connection between edgetoughnes...