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Partitions of graphs under distance ...

Emory University.

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Partitions of graphs under distance constraints.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Partitions of graphs under distance constraints./
作者:	Magnant, Colton.
面頁冊數:	119 p.
附註:	Adviser: Ronald Gould.
Contained By:	Dissertation Abstracts International69-04B.
標題:	Mathematics. -
電子資源:	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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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.
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773 0 $t Dissertation Abstracts International $g 69-04B.
790 $a 0665
790 1 0 $a Gould, Ronald, $e advisor
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856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3310272