Szabó Tibor: Sharp threshold for bounded degree spanning trees with many leaves
or a long bare path
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Abstract: We show that any given $n$-vertex tree with bounded maximum degree
and linearly many leaves is contained in the binomial random graph
$G(n,p)$ asymptotically almost surely for some $p=(1+o(1))\log n/n$.
Furthermore we also show that $G(n,p)$ contains asymptotically almost surely
every bounded degree spanning tree $T$ that has a path of linear length
whose vertices have degree two in $T$.
This represents joint work with Dan Hefetz and Michael Krivelevich.