no code implementations • 16 Dec 2020 • Rani Hod, Michael Krivelevich, Tobias Müller, Alon Naor, Nicholas Wormald
Pittel, Spencer and Wormald showed in 1996 that for any $k\ge3$ there exists an explicitly defined constant $c_{k}$ such that $p=c_{k}/n$ is the threshold function for the appearance of the $k$-core in $G(n, p)$.
Combinatorics Probability 05C80, 91A24
no code implementations • 9 Dec 2020 • Lior Gishboliner, Michael Krivelevich, Peleg Michaeli
As our main result, we show that under very mild conditions, the $r$-colour spanning-tree discrepancy of a graph $G$ is equal, up to a constant, to the minimum $s$ such that $G$ can be separated into $r$ equal parts by deleting $s$ vertices.
Combinatorics 05C35, 05D10, 11K38
