Hypergraph multiway cut problem is a problem of finding a minimum capacity set of hyperedges whose removal divides a given hypergraph into a specified number of connected componen...
The connectivity index w(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where is a real number ( = 0), and d(u) denotes the degree of the vertex u. Le...
: All information systems have to be protected. As the number of information objects and the number of users increase the task of information system's protection becomes more ...
Kasteleyn stated that the generating function of the perfect matchings of a graph of genus g may be written as a linear combination of 4g Pfaffians. Here we prove this statement. ...
Thomassen [9] conjectured that for all natural numbers k > 0 and m, every graph of minimum degree k + 1 contains a cycle of length congruent to 2m modulo k. We prove that this ...