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Title: Extensions of a theorem of Erdős on nonhamiltonian graphs
Abstract

Letbe integers with, and set. Erdős proved that when, eachn‐vertex nonhamiltonian graphGwith minimum degreehas at mostedges. He also provides a sharpness examplefor all such pairs. Previously, we showed a stability version of this result: fornlarge enough, every nonhamiltonian graphGonnvertices withand more thanedges is a subgraph of. In this article, we show that not only does the graphmaximize the number of edges among nonhamiltonian graphs withnvertices and minimum degree at leastd, but in fact it maximizes the number of copies of any fixed graphFwhennis sufficiently large in comparison withdand. We also show a stronger stability theorem, that is, we classify all nonhamiltoniann‐vertex graphs withand more thanedges. We show this by proving a more general theorem: we describe all such graphs with more thancopies offor anyk.

 
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NSF-PAR ID:
10051304
Author(s) / Creator(s):
 ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Journal of Graph Theory
Volume:
89
Issue:
2
ISSN:
0364-9024
Page Range / eLocation ID:
p. 176-193
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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