On decomposing complete tripartite graphs into 5-cycles

Decomposing Complete Tripartite Graphs into Closed Trails of Arbitrary Lengths

The complete tripartite graph Kn,n,n has 3n 2 edges. For any collection of positive integers x1, x2, . . . , xm with m ∑ i=1 xi = 3n 2 and xi > 3 for 1 6 i 6 m, we exhibit an edge-disjoint decomposition of Kn,n,n into closed trails (circuits) of lengths x1, x2, . . . , xm.

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.

Further decompositions of complete tripartite graphs into 5-cycles

Decomposing Complete Equipartite Graphs into Short Odd Cycles

In this paper we examine the problem of decomposing the lexicographic product of a cycle with an empty graph into cycles of uniform length. We determine necessary and sufficient conditions for a solution to this problem when the cycles are of odd length. We apply this result to find necessary and sufficient conditions to decompose a complete equipartite graph into cycles of uniform length, in t...

On Cyclic Decompositions of Complete Graphs into Tripartite Graphs

We introduce two new labelings for tripartite graphs and show that if a graph G with n edges admits either of these labelings, then there exists a cyclic G-decomposition of K2nx+1 for every positive integer x. We also show that if G is the union of two vertext-disjoint cycles of odd length, other than C3 ∪ C3, then G admits one of these labelings.