Abstract
Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most [n/k]. With regard to this conjecture, Chvátal and Szemérldi [2] 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. Our result is an improvement of this result.
| Original language | English |
|---|---|
| Pages (from-to) | 295-298 |
| Number of pages | 4 |
| Journal | Annals of Discrete Mathematics |
| Volume | 38 |
| Issue number | C |
| DOIs | |
| Publication status | Published - 1988 |
| Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
Cite this
Short Cycles in Digraphs. / Nishimura, Tsuyoshi.
In: Annals of Discrete Mathematics, Vol. 38, No. C, 1988, p. 295-298.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Short Cycles in Digraphs
AU - Nishimura, Tsuyoshi
PY - 1988
Y1 - 1988
N2 - Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most [n/k]. With regard to this conjecture, Chvátal and Szemérldi [2] 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. Our result is an improvement of this result.
AB - Caccetta and Häggkvist [1] conjectured that every digraph with n vertices and minimum outdegree k contains a directed cycle of length at most [n/k]. With regard to this conjecture, Chvátal and Szemérldi [2] 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. Our result is an improvement of this result.
UR - http://www.scopus.com/inward/record.url?scp=77957045838&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77957045838&partnerID=8YFLogxK
U2 - 10.1016/S0167-5060(08)70796-9
DO - 10.1016/S0167-5060(08)70796-9
M3 - Article
AN - SCOPUS:77957045838
VL - 38
SP - 295
EP - 298
JO - Annals of Discrete Mathematics
JF - Annals of Discrete Mathematics
SN - 0167-5060
IS - C
ER -