DECOMPOSITIONS OF $K_{m,n}$ INTO 4-CYCLES AND 8-CYCLES

Decompositions of Graphs into 5-Cycles and Other Small Graphs

In this paper we consider the problem of finding the smallest number q such that any graph G of order n admits a decomposition into edge disjoint copies of a fixed graph H and single edges with at most q elements. We solve the case when H is the 5-cycle, the 5-cycle with a chord and any connected non-bipartite non-complete graph of order 4.

Almost resolvable decompositions of 2Kn into cycles of odd length

The complete graph on n vertices is denoted by K, and the graph on n vertices in which each pair of vertices is joined by exactly 2 edges is denoted by 2K,. An m-cycle is a sequence of m distinct vertices (u1, u2, . . . . u,) such that ui is adjacent to ui+ 1 and U, is adjacent to u1 . A spanning subgraph H of G is a subgraph for which V(H) = V(G). An i-factor of a graph G is a spanning subgrap...

Cycle decompositions V: Complete graphs into cycles of arbitrary lengths

We show that the complete graph on n vertices can be decomposed into t cycles of specified lengths m1, . . . ,mt if and only if n is odd, 3 ≤ mi ≤ n for i = 1, . . . , t, and m1+· · ·+mt = ( n 2 ) . We also show that the complete graph on n vertices can be decomposed into a perfect matching and t cycles of specified lengths m1, . . . ,mt if and only if n is even, 3 ≤ mi ≤ n for i = 1, . . . , t...

Further decompositions of complete tripartite graphs into 5-cycles

Decompositions of complete tripartite graphs into k-cycles

We show that a complete tripartite graph with three partite sets of equal size m may be decomposed into k-cycles for any k 2: 3 if and only if k divides 3m2 and k ::; 3m.