Lower Bounds on the Odds Against Tree Spectral Sets

The path spectrum of a graph is the set of lengths of all maximal paths in the graph. A set S of positive lengths is tree spectral if it is the path spectrum of a tree. We show that for each even integer s⩾2 at least 34.57% of all subsets of the set {2,3,…,s} are tree spectral, and for each odd inte...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 38; pp. 559 - 564
Main Authors Levit, Vadim E., Tankus, David
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2011
Subjects
lower bound
maximal path
tree spectral set
maximal path
tree spectral set
lower bound
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Summary:The path spectrum of a graph is the set of lengths of all maximal paths in the graph. A set S of positive lengths is tree spectral if it is the path spectrum of a tree. We show that for each even integer s⩾2 at least 34.57% of all subsets of the set {2,3,…,s} are tree spectral, and for each odd integer s⩾2 at least 27.44% of all subsets of the set {2,3,…,s} are tree spectral.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2011.09.091