A one-factorization of a regular graph G is perfect if the union of any two one-factors is a Hamiltonian cycle. A graph G is said to be P1F if it possess a perfect one-factorization. We prove that G is a P1F cubic graph if and only if L(G) is a P1F quartic graph. Moreover, we give some necessary conditions for the existence of a P1F planar graph.
Given a one-factorization F of the complete bipartite graph Kn,n, let pf(F) denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in F . Let pf(n) be the maximum of pf(F) over all one-factorizations F of Kn,n. In this work we prove that p
Let G be a connected graph with vertex set V (G) = {v1, v2, · · · , vν} , which may have multiple edges but have no loops, and 2 ≤ dG(vi) ≤ 3 for i = 1, 2, · · · , ν, where dG(v) denotes the degree of vertex v of G. We show that if G has an even number of edges, then the number o
A perfectly one-factorable (P1F) regular graph G is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. We consider the case in which G is a cubic graph. The existence of a P1F cubic graph is guaranteed for
A perfectly one-factorable (P1F) regular graph is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. The case of cubic graphs is treated. The existence of a P1F cubic graph is guaranteed for each admissibl
We exploit the technique of Galvin (1995) to prove that an orientation D of a line-graph G (of a multigraph) is kernel-perfect if and only if every oriented odd cycle in D has a chord (or pseudochord) and every clique has a kernel. @ 1998 Elsevier Science B.V. All rights reserved
We construct seven new examples of perfect one-factorizations, in the complete graphs K170, K730. K1370. K1850t and K3126. These are generated by twoand four-quotient starters in finite fields. We also find several examples of perfect one-factorizations that are not isomorphic to