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Saturated Graphs of Prescribed Minimum Degree

Published online by Cambridge University Press:  07 December 2016

A. NICHOLAS DAY
A. NICHOLAS DAY*
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK (e-mail: [email protected])
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Abstract

A graph G is H-saturated if it contains no copy of H as a subgraph but the addition of any new edge to G creates a copy of H. In this paper we are interested in the function satt(n,p), defined to be the minimum number of edges that a Kp-saturated graph on n vertices can have if it has minimum degree at least t. We prove that satt(n,p) = tn − O(1), where the limit is taken as n tends to infinity. This confirms a conjecture of Bollobás when p = 3. We also present constructions for graphs that give new upper bounds for satt(n,p).

Keywords

05C35
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 26 , Issue 2 , March 2017 , pp. 201 - 207
Copyright
Copyright © Cambridge University Press 2016 

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