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Abstract for Tomasz \L uczak, On Ramsey Minimal Graphs

An elementary probabilistic argument is presented 
which shows  that for every forest~$F$ other than  a matching,
and  every graph $G$ containing a  cycle, there exists
an infinite number of graphs $J$ such that $J\to (F,G)$ but 
if we delete from $J$  any edge~$e$ the graph $J-e$ obtained in this 
way does not have this property.
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