# v-PATHS OF ARCS IN REGULAR MULTIPARTITE TOURNAMENTS

• Yao, Tianxing (Department of mathematics, Nanjing University) ;
• Guo, Yubao (Lehrstuhl C Fur Mathematik, RWTH Aachen) ;
• Zhang, Kemin (Department of mathematics, Nanjing University)
• Published : 1999.05.01

#### Abstract

A v-path of an arc xy in a multipartite tournament T is an oriented oath in T-y which starts at x such that y does not dominate and end vertex of the path. We show that if T is a regular n-partite (n$\geq$7) tournament, then every arc of T has a v-path of length m for all m satisfying 2$\leq$m$\leq$n-2. Our result extends the corresponding result for regular tournaments, due to Alspach, Reid and Roselle [2] in 1974, to regular multipartite tournaments.

#### References

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