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Cohesion and Non-separating Trees in connected graphs

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Date Issued:
2014
Summary:
If T is a tree on n vertices, n 3, and if G is a connected graph such that dudvd u,v 2n for every pair of distinct vertices of G, it has been conjectured that G must have a non-separating copy of T. In this note, we prove this result for the special case in which dudv du,v 2n 2 for every pair of distinct vertices of G, and improve this slightly for trees of diameter at least four and for some trees of diameter three. We also characterize the graphs on at most 8 vertices with dudvdu,v 7 for every pair of distinct vertices of G, and no non-separating copy of K_{1,3}
Title: Cohesion and Non-separating Trees in connected graphs.
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Name(s): Gottipati, Chenchu B.
Locke, Stephen C.
Graduate College
Type of Resource: text
Genre: Abstract
Date Created: 2014
Date Issued: 2014
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 1 p.
Language(s): English
Summary: If T is a tree on n vertices, n 3, and if G is a connected graph such that dudvd u,v 2n for every pair of distinct vertices of G, it has been conjectured that G must have a non-separating copy of T. In this note, we prove this result for the special case in which dudv du,v 2n 2 for every pair of distinct vertices of G, and improve this slightly for trees of diameter at least four and for some trees of diameter three. We also characterize the graphs on at most 8 vertices with dudvdu,v 7 for every pair of distinct vertices of G, and no non-separating copy of K_{1,3}
Identifier: FA00005818 (IID)
Collection: FAU Student Research Digital Collection
Note(s): The Fifth Annual Graduate Research Day was organized by Florida Atlantic University’s Graduate Student Association. Graduate students from FAU Colleges present abstracts of original research and posters in a competition for monetary prizes, awards, and recognition
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Sublocation: Digital Library
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Owner Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.