On the structure of strong 3-quasi-transitive digraphs
نویسندگان
چکیده
In this paper, D = (V (D), A(D)) denotes a loopless directed graph (digraph) with at most one arc from u to v for every pair of vertices u and v of V (D). Given a digraph D, we say that D is 3-quasi-transitive if, whenever u → v → w → z in D, then u and z are adjacent. In [3], Bang-Jensen introduced 3-quasi-transitive digraphs and claimed that the only strong 3quasi-transitive digraphs are the strong semicomplete digraphs and strong bipartite semicomplete digraphs. In this paper, we exhibit a family of strong 3-quasi-transitive digraphs distinct from strong semicomplete digraphs and strong bipartite semicomplete digraphs and provide a complete characterization of strong 3-quasi-transitive digraphs.
منابع مشابه
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010