Edge-disjoint Decompositions of Complete Multipartite Graphs into Gregarious Long Cycles

摘要

The notion of gregarious cycles in complete multipartite graphs was introduced by Billington and Hoffman in 2003 and was modified later by Billington, Hoffman, and Rodger and by Billington, Smith, and Hoffman. In this paper, we propose a new definition of gregarious cycles in complete multipartite graphs which generalizes all of the three definitions. With our definition, we can consider gregarious cycles of long length in complete multipartite graphs, and we show some results on the existence of edge-disjoint decompositions of complete multipartite graphs into gregarious long cycles.