A generalization of the Oberwolfach problem andCt-factorizations of complete equipartite graphs

A Remark on Circulant Decompositions of Complete Multipartite Graphs by Gregarious Cycles

“…The key factor for all these works was the decomposition of complete bipartite graphs obtained by Sotteau ([19]). Then, many authors began to consider cycle decompositions with special properties ( [4], [5], [12], [13]). Especially, Billington and Hoffman ( [2]) introduced the notion of gregarious cycles in tripartite graphs.…”

A note on the Hamilton–Waterloo problem with C8-factors and CmWang1, Cao2 2018Discrete Mathematics90100View full textAdd to dashboardCite

“…A factor of H is a spanning subgraph of H. Suppose G is a subgraph of H, a G-factor of H is a set of edge-disjoint subgraphs of H, each isomorphic to G. A G-factorization of H is a set of edge-disjoint G-factors of H. A C k -factorization of H is a partition of E(H) into C k -factors. Many papers introduced C k -factorization of K u [g], see [2,4,10,18,19,20,22,23]. Theorem 1.1.…”

The Hamilton-Waterloo Problem for C3-Factors and Cn-Factors

“…We denote the cycle of length k by C k , the complete graph on v vertices by K v , and the complete u-partite graph with u parts of size g by K u [g]. A factor of a graph H is a spanning subgraph of H. Suppose G is a subgraph of a graph H, a G-factor of H is a set of edge-disjoint subgraphs of H, each isomorphic to G. And a G-factorization of H is a set of edge-disjoint G-factors of H. Many authors [2,4,15,16,18,19,25,26] have contributed to prove the following result. Theorem 1.1.…”