# zbMATH — the first resource for mathematics

Powers of Hamilton cycles in tournaments. (English) Zbl 0712.05030
Let $$T_ n$$ denote a tournament with n nodes in which every node has indegree and outdegree at least $$(1/4+\epsilon)n$$; the authors show that such a tournament must contain the k-th power of a Hamilton cycle provided that n is sufficiently large, depending on $$\epsilon$$ and k.
Reviewer: J.W.Moon

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C45 Eulerian and Hamiltonian graphs
##### Keywords:
degrees; tournament; Hamilton cycle
Full Text:
##### References:
 [1] Bollobás, B, Extremal theory, () · Zbl 0165.57303 [2] Erdős, P, On extremal problems of graphs and generalised graphs, Israel J. math., 2, 183-190, (1964) · Zbl 0129.39905 [3] \scR. Häggkvist, Hamilton cycles in oriented graphs, to appear. [4] Jackson, B, Long paths and cycles in oriented graphs, J. graph. theory, 5, 145-157, (1981) · Zbl 0458.05041 [5] Thomassen, C, Edge-disjoint Hamiltonian paths and cycles in tournaments, (), 151-168 · Zbl 0486.05049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.