Hamilton Cycle Rich 2-Factorization of Complete Equipartite Graphs-II

摘要

For any given two 2-factors G and H of a complete p-partite graph K(m, p), with m vertices in each partite set, we prove the existence of a 2-factorization of K(m, p), in which one 2-factor is isomorphic to G, another 2-factor is isomorphic to H and the remaining 2-factors are hamilton cycles. Further, we prove the corresponding result for K(m, p) − I, where I is a 1-factor of K(m, p), when K(m, p) is an odd regular graph. In fact our results together with the results of McCauley and Rodger settled the problem of 2-factorization of K(m, p), when two of the 2-factors are isomorphic to the given two 2-factors and the remaining 2-factors are hamilton cycles except for (m, p) = (m, 2).