Girth in digraphs
β Scribed by J. C. Bermond; A. Germa; M. C. Heydemann; D. Sotteau
- Publisher
- John Wiley and Sons
- Year
- 1980
- Tongue
- English
- Weight
- 211 KB
- Volume
- 4
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
For an integer k > 2, the best function m(n, k) is determined such that every strong digraph of order n with at least m(n, k) arcs contains a circuit of length k or less.
π SIMILAR VOLUMES
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We define a fractional version of the notion of ``kernels'' in digraphs and prove that every clique acyclic digraph (i.e., one in which no clique contains a cycle) has a fractional kernel. Using this we give a short proof of a recent result of Boros and Gurvich (proving a conjecture of Berge and Duc
Let c be the smallest possible value such that every digraph on n vertices with minimum outdegree at least cn contains a directed triangle. It was conjectured by Caccetta and Ha ggkvist in 1978 that c=1Γ3. Recently Bondy showed that c (2 -6&3)Γ5=0.3797... by using some counting arguments. In this no
Let G be 2-connected graph with girth g and minimum degree d. Then each, pair of verticfs of G is joined by a path of length a t least maxi? (dl)g, ( d -?) (g -4) + 2) if g B 4, and the length of a longest cycle of G is at least max{[(d -1) (g -2) + 21, [(2d -3) (g -4) + 41).
## Abstract A hypotraceable digraph is a digraph __D__ = (__V, E__) which is not traceable, i.e., does not contain a (directed)Hamiltonian path, but for which __D__ β __v__ is traceable for all __ve__ β __V__. We prove that a hypotraceable digraph of order __n__ exists iff __n__ β₯ 7 and that for ea