The asymptotic number of claw-free cubic graphs

Let H n be the number of claw-free cubic graphs on 2 n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for H n . Here we determine the asymptotic behavior of this sequence: H n∼ (2n)! e 6πn n 2e n/3 e (n/2) 1/3 . We have verified this form...

Full description

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 272; no. 1; pp. 107 - 118
Main Authors McKay, Brendan D., Palmer, Edgar M., Read, Ronald C., Robinson, Robert W.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 28.10.2003
Elsevier
Subjects
Asymptotic enumeration
Claw-free
Combinatorics
Combinatorics. Ordered structures
Cubic graphs
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Claw-free
Cubic graphs
Asymptotic enumeration
Graph theory
Claw free graph
Enumeration
Cubic graph
Asymptotic behavior
Online AccessGet full text

Cover

More Information
Summary:Let H n be the number of claw-free cubic graphs on 2 n labeled nodes. In an earlier paper we characterized claw-free cubic graphs and derived a recurrence relation for H n . Here we determine the asymptotic behavior of this sequence: H n∼ (2n)! e 6πn n 2e n/3 e (n/2) 1/3 . We have verified this formula using known asymptotic estimates of cubic graphs with loops and multiple edges and also by the method of inclusion and exclusion.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(03)00188-2