Lower Bounds on the Odds Against Tree Spectral Sets

Vadim E. Levit; David Tankus

doi:10.1016/j.endm.2011.09.091

Lower Bounds on the Odds Against Tree Spectral Sets

Vadim E. Levit
, David Tankus

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	559-564
Number of pages	6
Journal	Electronic Notes in Discrete Mathematics
Volume	38
DOIs	https://doi.org/10.1016/j.endm.2011.09.091
State	Published - 1 Dec 2011

Keywords

Lower bound
Maximal path
Tree spectral set

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10.1016/j.endm.2011.09.091

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abstract = "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.",

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AB - 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.

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JO - Electronic Notes in Discrete Mathematics

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Lower Bounds on the Odds Against Tree Spectral Sets

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Keywords

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