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

Loading next page...
 
/lp/springer_journal/on-min-max-pair-in-tournaments-NP50YtCeD1
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Japan KK, part of Springer Nature
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

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off