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Vicarious Graphs

Published online by Cambridge University Press:  13 November 2009

TOMASZ ŁUCZAK  and
ANDREW THOMASON
TOMASZ ŁUCZAK
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland (e-mail: tomasz@amu.edu.pl)
ANDREW THOMASON
Affiliation:
DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK (e-mail: A.G.Thomason@dpmms.cam.ac.uk)
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Abstract

Let H be some fixed graph. We call a graph Gvicarious for H if G is maximal H-free and, for every edge e of G, there is an edge f not in G such that G − e + f is also H-free. We demonstrate various properties of vicarious graphs and several examples are given. It is conjectured that a graph of order n which is vicarious for K3 has size at most (1/4 + o(1))().

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 5-6: Papers from the 2009 Oberwolfach Meeting on Combinatorics and Probability , November 2010 , pp. 819 - 827
Copyright
Copyright © Cambridge University Press 2009

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References

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