BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiaao Li (Nankai University) DTSTART:20201029T070000Z DTEND:20201029T080000Z DTSTAMP:20260423T021016Z UID:SCMSComb/17 DESCRIPTION:Title: Flows and Cycle Covers of Signed Graphs\nby Jiaao Li (Nankai Univers ity) as part of SCMS Combinatorics Seminar\n\n\nAbstract\nFlow theory of s igned graphs was introduced by Bouchet as dual notion to local tensions of graphs embedded on non-orientable surfaces\, which generalized Tutte's fl ow theory of ordinary graphs. Recently\, we prove that every flow-admissib le signed graph admits a nowhere-zero balanced $Z_2\\times Z_3$-flow. This extends Seymour's 6-flow theorem from ordinary graphs (which are signed g raphs without unbalanced circuit) to long-barbell-free signed graphs (whic h are signed graphs without vertex-disjoint unbalanced circuits). In this talk\, we will show how to apply this theorem to extend some classical res ults on flow and cycle decomposition/cover\, due to Jaeger\, Fan\, Alon-Ta rsi\, etc.\, to some signed graphs. Those classical results may not be tig ht for ordinary graphs\, whose expected improvements are known as Tutte's $5$-flow Conjecture\, Berge-Fulkerson Conjecture\, Cycle Double Cover Conj ecture and Shortest Cycle Cover Conjecture. In contrast\, we shall see tha t the signed analogies of those classical results are indeed sharp for cer tain signed graphs.\n\npassword 121323\n LOCATION:https://researchseminars.org/talk/SCMSComb/17/ END:VEVENT END:VCALENDAR