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2004•Journal of Shanxi UniversityRequires access

Pancyclic Out-arcs of a Vertex in Not Round-decomposable Local Tournament

Shengjia Li

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Abstract

Yao Tianxing (Discrete Appl.Math.2000,99:245-249) proved that every strong tournament contains an out-arc-pancyclic vertex.In this paper,the result of Yao Tianxing is extended to local tournament and the corresponding result is that if a strong and not round-decomposable proper local tournament T has a strong minimal separating set S such that T-S is not semicomplete,then there is a 4-out-arc-pancyclic vertex of T.

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What this paper is about

Yao Tianxing (Discrete Appl.Math.2000,99:245-249) proved that every strong tournament contains an out-arc-pancyclic vertex.In this paper,the result of Yao Tianxing is extended to local tournament and the corresponding result is that if a strong and not round-decomposable proper local tournament T has a strong minimal separating set S such that T-S is not semicomplete,then there is a 4-out-arc-pancyclic vertex of T.

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Available abstract

Yao Tianxing (Discrete Appl.Math.2000,99:245-249) proved that every strong tournament contains an out-arc-pancyclic vertex.In this paper,the result of Yao Tianxing is extended to local tournament and the corresponding result is that if a strong and not round-decomposable proper local tournament T has a strong minimal separating set S such that T-S is not semicomplete,then there is a 4-out-arc-pancyclic vertex of T.

Key concepts: Tournament, Vertex (graph theory), Arc (geometry), Combinatorics, Mathematics, Discrete mathematics, Graph, Geometry

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