On Min–Max Pair in Tournaments

On Min–Max Pair in Tournaments Let T be a tournament of order \$\$n\ge 3\$\$ n ≥ 3 . A pair of distinct vertices x, y of T is called a min–max pair if one of x and y is of minimum out-degree, while the other is of maximum out-degree. Let xy be an arc such that x, y is a min–max pair. We call xy a min–max arc if x has minimum out-degree, and max–min arc otherwise. We prove that if yx is a min–max arc, then there exists a hamiltonian path from x to y; if xy is a max–min arc, then there exists a hamiltonian path from x to y with the exception of a few cases. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Graphs and Combinatorics Springer Journals

On Min–Max Pair in Tournaments

, Volume 34 (4) – May 31, 2018
6 pages

/lp/springer_journal/on-min-max-pair-in-tournaments-NP50YtCeD1
Publisher
Springer Journals
Subject
Mathematics; Combinatorics; Engineering Design
ISSN
0911-0119
eISSN
1435-5914
D.O.I.
10.1007/s00373-018-1899-3
Publisher site
See Article on Publisher Site

Abstract

Let T be a tournament of order \$\$n\ge 3\$\$ n ≥ 3 . A pair of distinct vertices x, y of T is called a min–max pair if one of x and y is of minimum out-degree, while the other is of maximum out-degree. Let xy be an arc such that x, y is a min–max pair. We call xy a min–max arc if x has minimum out-degree, and max–min arc otherwise. We prove that if yx is a min–max arc, then there exists a hamiltonian path from x to y; if xy is a max–min arc, then there exists a hamiltonian path from x to y with the exception of a few cases.

Journal

Graphs and CombinatoricsSpringer Journals

Published: May 31, 2018

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