It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bi-partite graph K n,n with a perfect matching removed can be covered by k bicliques, then n ≤ k k 2. We give a slightly simplified proof and we show that the result is tight. Moreover we use the result to prove analogous bounds for coverings of some other classes of graphs by… (More)
The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's Theorem, the strong isometric dimension of the Hamming graphs K 2 K n is determined.
A generalized prism, or more specifically an (0, j)-prism of order 2n (where n is even) is a cubic graph consisting of two cycles u The question of factorization of complete bipartite graphs into (0, j)-prisms was completely settled by the author and S. Cichacz. Some partial results have also been obtained by them and P. Kovar and S. Dib. We will present a… (More)
We give a complete characterization of trees with at most four non-leave vertices, which factorize the complete graph K 2n .