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Partitions of graphs under distance ...

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Partitions of graphs under distance constraints.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Partitions of graphs under distance constraints./
Author:	Magnant, Colton.
Description:	119 p.
Notes:	Adviser: Ronald Gould.
Contained By:	Dissertation Abstracts International69-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3310272
ISBN:	9780549587453

Partitions of graphs under distance constraints.
Magnant, Colton.

Partitions of graphs under distance constraints. - 119 p.

Adviser: Ronald Gould.

Thesis (Ph.D.)--Emory University, 2008.

Let G be a graph of order n and t ≥ 3 be an integer. Recently, Kaneko and Yoshimoto [24] provided a sharp minimum degree condition such that for any set X of t vertices, G contains a hamiltonian cycle H so that the distance along H between any two vertices of X is at least n/2t. Also, Enomoto and Ota [13] conjectured that with a sufficient degree sum, for any set of t chosen vertices, a graph can be partitioned into paths of prescribed lengths beginning at the chosen set of vertices. With these results as motivation, we provide sharp minimum degree and degree sum conditions for a variety of graph partitions.

ISBN: 9780549587453Subjects--Topical Terms:

515831
Mathematics.

Partitions of graphs under distance constraints.
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008 100802s2008 ||||||||||||||||| ||eng d
020 $a 9780549587453
035 $a (UMI)AAI3310272
035 $a AAI3310272
040 $a UMI $c UMI
100 1 $a Magnant, Colton. $3 1035800
245 1 0 $a Partitions of graphs under distance constraints.
300 $a 119 p.
500 $a Adviser: Ronald Gould.
500 $a Source: Dissertation Abstracts International, Volume: 69-04, Section: B, page: 2360.
502 $a Thesis (Ph.D.)--Emory University, 2008.
520 $a Let G be a graph of order n and t ≥ 3 be an integer. Recently, Kaneko and Yoshimoto [24] provided a sharp minimum degree condition such that for any set X of t vertices, G contains a hamiltonian cycle H so that the distance along H between any two vertices of X is at least n/2t. Also, Enomoto and Ota [13] conjectured that with a sufficient degree sum, for any set of t chosen vertices, a graph can be partitioned into paths of prescribed lengths beginning at the chosen set of vertices. With these results as motivation, we provide sharp minimum degree and degree sum conditions for a variety of graph partitions.
520 $a Given an ordered set of t vertices in G and a set of t distances, we find a sharp degree condition for G to contain a hamiltonian cycle with the t vertices in order with approximately the corresponding prescribed distances between them. We also show similar results for partitioning the graph into paths between chosen vertices or paritioning into cycles containing chosen vertices, all of approximately prescribed lengths.
590 $a School code: 0665.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a Emory University. $3 1017429
773 0 $t Dissertation Abstracts International $g 69-04B.
790 $a 0665
790 1 0 $a Gould, Ronald, $e advisor
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3310272