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UID:a5ec76c880bbeee5acdaeb6a1329ea60
CATEGORIES:Graduate Student Combinatorics Seminar Sponsored by DIMACS
CREATED:20241024T131501
SUMMARY:The Small Quasikernel Conjecture
LOCATION:HLL-701
DESCRIPTION:
CONTACT:Sam Spiro
X-EXTRAINFO:Abstract: Given a digraph $D$, we say that a set of vertices $Q\subseteq V(
 D)$ is a quasikernel if $Q$ is an independent set and if every vertex of $D
 $ can be reached from $Q$ by a path of length at most 2.  The Small Quasike
 rnel Conjecture of P.L.\ Erd\H{o}s and Sz\'ekely from 1976 states that ever
 y $n$-vertex source-free digraph $D$ contains a quasikernel of size at most
  $\frac{1}{2}n$.  Despite being posed nearly 50 years ago, very little is k
 nown about this conjecture, with the only non-trivial upper bound of $n-\fr
 ac{1}{4}\sqrt{n\log n}$ being proven very recently by ourself.  We discuss 
 this together with a number of other related results and open problems arou
 nd the Small Quasikernel Conjecture.
DTSTAMP:20260828T122120
DTSTART;TZID=America/New_York:20241030T121500
DTEND;TZID=America/New_York:20241030T131500
SEQUENCE:0
TRANSP:OPAQUE
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