Longest cycles in almost regular 3-partite tournaments
نویسندگان
چکیده
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.
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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...
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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-...
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A tournament is an orientation of a complete graph and a multipartite or c-partite tournament is an orientation of a complete c-partite graph. If D is a digraph, then let d + (x) be the outdgree and d ? (x) the indegree of the vertex x in D. The minimum (maximum) out-degree and the minimum (maximum) indegree of D are denoted by + ((+) and ? ((?), respectively. In addition, we deene = minf + ; ?...
متن کاملLongest Cycles in 3-connected 3-regular Graphs
I n t r o d u c t i o n . In this paper, we s tudy the following quest ion: How long a cycle must there be in a 3-connected 3-regular graph on n vertices? For planar graphs this question goes back to T a i t [6], who conjectured tha t any planar 3-connected 3-regular graph is hamiltonian. T u t t e [7] disproved this conjecture by finding a counterexample on 46 vertices. Using Tu t t e ' s exam...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.04.030