BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Asaf Ferber (UC Irvine) DTSTART:20200615T130000Z DTEND:20200615T140000Z DTSTAMP:20260423T052451Z UID:EPC/10 DESCRIPTION:Title: Ind uced subgraphs with prescribed degrees mod q\nby Asaf Ferber (UC Irvin e) as part of Extremal and probabilistic combinatorics webinar\n\n\nAbstra ct\nA classical result of Galai asserts that the vertex-set of every graph can be partitioned into two sets such that each induces a graph with all degrees even. Scott studied the (harder) problem of \ndet ermining for which graphs can we find a partition into arbitrary many part s\, each of which induces a graph with all odd degrees.\n\nIn this talk we discuss various extensions of this problem to arbitrary residues mod $q\\ geq 3$. Among other results\, we show that for every $q$\, a typical graph $G(n\,1/2)$ can be equi-partitioned (up to divisibility conditions) into $q+1$ sets\, each of which spans a graph with a prescribed degree sequence .\n \nSwitching to a completely unrelated problem: based on idea of the main key lemma of th e above results\, we give non-trivial bound (but weaker than known results ) on the singularity probability of a random symmetric Bernoulli matrix. T he new argument avoids both decoupling and distance from random hyperplane s and it turns this problem into a simple and elegant exercise.\n \nThe first part of the ta lk is based on a joint work with Liam Hardiman (UCI) and Michael Krivelevi ch (Tel Aviv University).\n LOCATION:https://researchseminars.org/talk/EPC/10/ END:VEVENT END:VCALENDAR