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

نویسندگان

  • Gregory Gutin
  • Arash Rafiey
چکیده

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.

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

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

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

Weakly Complementary Cycles in 3-Connected Multipartite Tournaments

The vertex set of a digraph D is denoted by V (D). A c-partite tournament is an orientation of a complete c-partite graph. A digraph D is called cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (D) = V (C1) ∪ V (C2), and a multipartite tournament D is called weakly cycle complementary if there exist two vertex disjoint cycles C1 and C2 such that V (C1) ∪ V (C2...

متن کامل

Notes on cycles through a vertex or an arc in regular 3-partite tournaments

We shall assume that the reader is familiar with standard terminology on directed graphs (see, e.g., Bang-Jensen and Gutin [1]). In this note, if we speak of a cycle, then we mean a directed cycle. If xy is an arc of a digraph D, then we write x → y and say x dominates y. If X and Y are two disjoint vertex sets of a digraph D such that every vertex of X dominates every vertex of Y , then we say...

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

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:
  • Discrete Mathematics

دوره 289  شماره 

صفحات  -

تاریخ انتشار 2004