TY - JOUR

T1 - Lower Bounds on the Odds Against Tree Spectral Sets

AU - Levit, Vadim E.

AU - Tankus, David

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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.

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.

KW - Lower bound

KW - Maximal path

KW - Tree spectral set

UR - http://www.scopus.com/inward/record.url?scp=82955220218&partnerID=8YFLogxK

U2 - 10.1016/j.endm.2011.09.091

DO - 10.1016/j.endm.2011.09.091

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AN - SCOPUS:82955220218

SN - 1571-0653

VL - 38

SP - 559

EP - 564

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -