منابع مشابه
Directed Triangles in Digraphs
A particularly interesting special case that is still open is: any digraph on n vertices with minimum outdegree at least n 3 contains a directed triangle. Short of proving this, one may seek a value c as small as possible such that every digraph on n vertices with minimum outdegree at least cn contains a directed triangle. This was the strategy of Caccetta and Ha ggkvist [3], who showed that c ...
متن کاملOn Directed Triangles in Digraphs
Using a recent result of Chudnovsky, Seymour, and Sullivan, we slightly improve two bounds related to the Caccetta-Haggkvist Conjecture. Namely, we show that if α ≥ 0.35312, then each n-vertex digraph D with minimum outdegree at least αn has a directed 3-cycle. If β ≥ 0.34564, then every n-vertex digraph D in which the outdegree and the indegree of each vertex is at least βn has a directed 3-cy...
متن کاملDirected triangles in directed graphs
We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n=t where t = 2:888997 : : : contains a directed circuit of length at most 3. c © 2003 Elsevier B.V. All rights reserved.
متن کاملReturnability in complex directed networks (digraphs)
The concept of returnability is proposed for complex directed networks (digraphs). It can be seen as a generalization of the concept of reciprocity. Two measures of the returnability are introduced. We establish closed formulas for the calculation of the returnability measures, which are also related to the digraph spectrum. The two measures are calculated for simple examples of digraphs as wel...
متن کاملMaximum directed cuts in acyclic digraphs
It is easily shown that every digraph with m edges has a directed cut of size at least m/4, and that 1/4 cannot be replaced by any larger constant. We investigate the size of a largest directed cut in acyclic digraphs, and prove a number of related results concerning cuts in digraphs and acyclic digraphs.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1998
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1839