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

  1. Canad. Math. Bull. v.10 Cycles of each length in regular tournaments B. Alspach
  2. J. Combin. Theory Ser. v.B17 Bypasses in asymmetric digraphs B. Alspach;K. B. Reid;D. P. Roselle
  3. Discrete Appl. Math. Outpaths in semicomplete multipartite digraphs Y. Guo
  4. J. Korean Math. Soc. v.36 Bypaths in local tournaments Y. Guo
  5. Discrete Appl. Math. v.79 Bypaths in tournaments Y. Guo;L. Volkmann
  6. J. Combin. Theory Ser. v.B28 Hamiltonian-connected tournaments C. Thomassen