Packing Digraphs with Directed Closed Trails

PAUL BALISTER
2003 Combinatorics, probability & computing  
It has been shown [Balister, 2001] that if n is odd and m 1 , . . . , mt are integers with m i ≥ 3 and t i=1 m i = |E(Kn)| then Kn can be decomposed as an edge-disjoint union of closed trails of lengths m 1 , . . . , mt. This result was later generalized [Balister, to appear] to all sufficiently dense Eulerian graphs G in place of Kn. In this article we consider the corresponding questions for directed graphs. We show that the compete directed graph ↔ Kn can be decomposed as an edge-disjoint
more » ... on of directed closed trails of lengths m 1 , . . . , mt whenever m i ≥ 2 and m i = |E( ↔ Kn)|, except for the single case when n = 6 and all m i = 3. We also show that sufficiently dense Eulerian digraphs can be decomposed in a similar manner, and we prove corresponding results for (undirected) complete multigraphs. Date
doi:10.1017/s0963548302005461 fatcat:cuhdzlqfbnbdxbnyqtywa4rgjq