On n-partite Tournaments with Unique n-cycle

نویسندگان

  • Gregory Gutin
  • Arash Rafiey
  • Anders Yeo
چکیده

An n-partite tournament is an orientation of a complete n-partite graph. An npartite tournament is a tournament, if it contains exactly one vertex in each partite set. Douglas, Proc. London Math. Soc. 21 (1970) 716-730, obtained a characterization of strongly connected tournaments with exactly one Hamilton cycle (i.e., n-cycle). For n ≥, we characterize strongly connected n-partite tournaments that are not tournaments with exactly one n-cycle. For n ≥ 5, we enumerate such non-isomorphic n-partite tournaments.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

When n-cycles in n-partite tournaments are longest cycles

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

متن کامل

Multipartite tournaments with small number of cycles

L. Volkmann, Discrete Math. 245 (2002) 19-53 posed the following question. Let 4 ≤ m ≤ n. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n − m + 1 cycles of length m? We answer this question in affirmative. We raise the following problem. Given m ∈ {3, 4, . . . , n}, find a characterization of strong n-partite tournaments having exactly n −m + 1 cycle...

متن کامل

Cycles through a given arc in almost regular multipartite tournaments

If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...

متن کامل

On the 3-kings and 4-kings in multipartite tournaments

Koh and Tan gave a sufficient condition for a 3-partite tournament to have at least one 3-king in [K.M. Koh, B.P. Tan, Kings in multipartite tournaments, Discrete Math. 147 (1995) 171–183, Theorem 2]. In Theorem 1 of this paper, we extend this result to n-partite tournaments, where n 3. In [K.M. Koh, B.P. Tan, Number of 4-kings in bipartite tournaments with no 3-kings, Discrete Math. 154 (1996)...

متن کامل

On Cycles Containing a Given Arc in Regular Multipartite Tournaments

In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . , n. Our result, in a sense, generalizes a theorem due to Alspach.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Graphs and Combinatorics

دوره 22  شماره 

صفحات  -

تاریخ انتشار 2006