×

Two complementary circuits in two-connected tournaments. (English) Zbl 0573.05031

Cycles in graphs, Workshop Simon Fraser Univ., Burnaby/Can. 1982, Ann. Discrete Math. 27, 321-334 (1985).
[For the entire collection see Zbl 0563.00004.]
The author proves that if T is a strong n-tournament, \(n\geq 6\), such that T-x is strong for every vertex x in T, then either T contains a 3-circuit and an (n-3)-circuit which are vertex disjoint or T is the unique 7- tournament which contains no transitive 4-subtournament. This result is best possible in the sense that many 1-connected tournaments need not contain two complementary circuits and may be considered as a first step towards the general problem of partitioning a highly connected tournament into two subtournaments of high connectivity.
Reviewer: M.Hager

MSC:

05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C40 Connectivity

Citations:

Zbl 0563.00004