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
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 ...
The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In t...
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...