A homogeneous set is a non-trivial module of a graph, i.e. a nonempty, non-unitary, proper vertex subset such that all its elements present the same outer neighborhood. Given two ...
Claudson F. Bornstein, Celina M. Herrera de Figuei...
We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variable...
In this paper, we prove that cyclic hamiltonian cycle systems of the complete graph minus a 1-factor, Kn - I, exist if and only if n 2, 4( mod 8) and n = 2p with p
Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n +I denote Kn,n with a 1-factor added. It is proved in this paper that there exists an m-c...
This paper presents a construction of a minimum cycle basis for the direct product of two complete graphs on three or more vertices. With the exception of two special cases, such ...