Decompositions of Graphs into 5-Cycles and Other Small Graphs

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

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 gregar...

Vertex Removable Cycles of Graphs and Digraphs

‎In this paper we defined the vertex removable cycle in respect of the following‎, ‎if $F$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$G in F $‎, ‎the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $.‎ ‎The vertex removable cycles of eulerian graphs are studied‎. ‎We also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎    

0n removable cycles in graphs and digraphs

In this paper we define the removable cycle that, if $Im$ is a class of graphs, $Gin Im$, the cycle $C$ in $G$ is called removable if $G-E(C)in Im$. The removable cycles in Eulerian graphs have been studied. We characterize Eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for Eulerian graph to have removable cycles h...

Further decompositions of complete tripartite graphs into 5-cycles

Even cycle decompositions of 4-regular graphs and line graphs

An even cycle decomposition of a graph is a partition of its edge into even cycles. We first give some results on the existence of even cycle decomposition in general 4-regular graphs, showing that K5 is not the only graph in this class without such a decomposition. Motivated by connections to the cycle double cover conjecture we go on to consider even cycle decompositions of line graphs of 2-c...