Hostname: page-component-7f64f4797f-kjzhn Total loading time: 0 Render date: 2025-11-04T14:42:46.065Z Has data issue: false hasContentIssue false
  • English
  • Français

Hamiltonian Cycles Avoiding Prescribed Arcs in Tournaments

Published online by Cambridge University Press:  01 September 1997

JØRGEN BANG-JENSEN ,
GREGORY GUTIN  and
ANDERS YEO
JØRGEN BANG-JENSEN
Affiliation:
Department of Mathematics and Computer Science, Odense University, Odense, Denmark (e-mail: jbj@imada.ou.dk, z.g.gutin@brunel.ac.uk, gyeo@imada.ou.dk)
GREGORY GUTIN
Affiliation:
Department of Mathematics and Computer Science, Odense University, Odense, Denmark (e-mail: jbj@imada.ou.dk, z.g.gutin@brunel.ac.uk, gyeo@imada.ou.dk)
ANDERS YEO
Affiliation:
Department of Mathematics and Computer Science, Odense University, Odense, Denmark (e-mail: jbj@imada.ou.dk, z.g.gutin@brunel.ac.uk, gyeo@imada.ou.dk)
Get access Rights & Permissions [Opens in a new window]

Abstract

Thomassen [6] conjectured that if I is a set of k−1 arcs in a k-strong tournament T, then T−I has a Hamiltonian cycle. This conjecture was proved by Fraisse and Thomassen [3]. We prove the following stronger result. Let T=(V, A) be a k-strong tournament on n vertices and let X1, X2, [ctdot ], Xl be a partition of the vertex set V of T such that [mid ]X1[mid ][les ][mid ]X2[mid ][les ][ctdot ][les ][mid ]Xl[mid ]. If k[ges ][sum ]l−1i=1[lfloor][mid ]Xi[mid ]/2[rfloor]+[mid ]Xl[mid ], then T−∪li=1{xy∈A[ratio ]x, y∈Xi} has a Hamiltonian cycle. The bound on k is sharp.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 6 , Issue 3 , September 1997 , pp. 255 - 261
Copyright
1997 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable