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 -