## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, December 19, 2006, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Paul Balister (Department of Mathematical Sciences, Univ. of Memphis)

## Cycle Decompositions

The Alspach conjecture proposes necessary and sufficient conditions for a complete graph $K_n$ ($n$ odd) or a complete graph minus a 1-factor ($n$ even) to be decomposable as an edge-disjoint union of cycles of prescribed lengths. We discuss various results on this and some related problems. In particular we show that the obvious necessary conditions are sufficient if the cycle lengths are bounded by a linear function of the number of vertices $n$, or in general if we only require closed trails of prescribed lengths rather than cycles. We also describe some similar results for complete bipartite graphs, dense graphs, and complete digraphs.

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