Short cycles in digraphs
Reads0
Chats0
TLDR
This work has proved that if G is a digraph with n vertices and if each of these vertices has outdegree at least k, then G contains a cycle of length at most (n/k) +2500.About:
This article is published in Discrete Mathematics.The article was published on 1988-12-01 and is currently open access. It has received 34 citations till now.read more
Citations
More filters
Book
Digraphs Theory Algorithms And Applications
Jrgen Bang-Jensen,Gregory Gutin +1 more
TL;DR: Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.
Journal ArticleDOI
Counting subgraphs: a new approach to the Caccetta-Ha¨ggkvist conjecture
Journal ArticleDOI
On the girth of digraphs
TL;DR: A short, self-contained proof of Caccetta and Haggkvist's result that the girth of every digraph with n vertices and minimum outdegree r is at most max⌈n/r⌉,2r−2 is obtained.
Journal ArticleDOI
Some Parameterized Problems On Digraphs
TL;DR: A survey results and open questions on complexity of parameterized problems on digraphs and some new results are proved on parameterizations of the backward paired comparison problem.
Journal ArticleDOI
On the Caccetta-Haggkvist Conjecture with Forbidden Subgraphs
TL;DR: In this paper, the Caccetta-Haggkvist conjecture for the case l = 3 was shown to hold for all known extremal examples of the C3 conjecture.
References
More filters
Journal ArticleDOI
Short cycles in directed graphs
Vašek Chvátal,Endre Szemerédi +1 more
TL;DR: It is proved that every directed graph with n vertices and minimum outdegree k contains a directed cycle of length at most nk + 2500.
Journal ArticleDOI
A note on the girth of digraphs
TL;DR: It is proved that a digraph of ordern and halfdegree ≧4 has girth not exceeding [n / 4], which is an application of the theory of connectivity of digraphs.