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The complete closure of a graph

✍ Scribed by Ralph Faudree; Odile Favaron; Evelyne Flandrin; Hao Li

Book ID
102892396
Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
677 KB
Volume
17
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We define the complete closure number cc(G) of a graph G of order n as the greatest integer k ≀ 2n βˆ’ 3 such that the __k__th Bondy‐ChvΓ‘tal closure Cl~k~(G) is complete, and give some necessary or sufficient conditions for a graph to have cc(G) = k. Similarly, the complete stability cs(P) of a property P defined on all the graphs of order n is the smallest integer k such that if Cl~k~(G) is complete then G satisfies P. For some properties P, we compare cs(P) with the classical stability s(P) of P and show that cs(P) may be far smaller than s(P). Β© 1993 John Wiley & Sons, Inc.

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