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- W2037123402 abstract "An outpath of a vertex x (an arc xy , respectively) in a digraph is a directed path starting at x ( xy , respectively) such that x dominates the endvertex of the path only if the endvertex also dominates x. Firstly, we show that if D is a strongly connected semicomplete n-partite ( n ⩾3) digraph, then every vertex v of D has an outpath of length k −1 for all k ∈{3,4,…, n }. Our result generalizes a theorem of Moon (Canad. Math. Bull. 9 (1966) 297–301) for tournaments. Secondly, we show that if T is a regular n-partite ( n ⩾3) tournament, then every arc of T has an outpath of length k −1 for all k satisfying 3⩽ k ⩽ n . This result extends a theorem of Alspach (Canad. Math. Bull. 10 (1967) 283–286) for regular tournaments to regular multipartite tournaments." @default.
- W2037123402 created "2016-06-24" @default.
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- W2037123402 date "1999-07-01" @default.
- W2037123402 modified "2023-09-29" @default.
- W2037123402 title "Outpaths in semicomplete multipartite digraphs" @default.
- W2037123402 doi "https://doi.org/10.1016/s0166-218x(99)00080-3" @default.
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