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Girth in digraphs

✍ 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.

✦ 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.


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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).

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## 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__ ‐ __v__ is traceable for all __ve__ ∈ __V__. We prove that a hypotraceable digraph of order __n__ exists iff __n__ β‰₯ 7 and that for ea