BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joonkyung Lee (Universität Hamburg) DTSTART:20200601T130000Z DTEND:20200601T140000Z DTSTAMP:20260423T035419Z UID:EPC/8 DESCRIPTION:Title: On t ripartite common graphs\nby Joonkyung Lee (Universität Hamburg) as pa rt of Extremal and probabilistic combinatorics webinar\n\n\nAbstract\nA gr aph $H$ is common if the number of monochromatic copies of $H$ in a 2-edge -colouring of the complete graph $K_N$ is minimised by the random colourin g. Burr and Rosta\, extending a famous conjecture by Erdős\, conjectured that every graph is common\, which was disproved by Thomason and by Sidore nko in late 1980s. Collecting new examples for common graphs had not seen much progress since then\, although very recently\, a few more graphs are verified to be common by the flag algebra method or the recent progress on Sidorenko's conjecture.\n\nOur contribution here is to give a new class o f tripartite common graphs. The first example class is so-called triangle trees\, which generalises two theorems by Sidorenko and hence answers a qu estion by Jagger\, Šťovíček\, and Thomason from 1996. We also prove t hat\, somewhat surprisingly\, given any tree T\, there exists a triangle t ree such that the graph obtained by adding $T$ as a pendant tree is still common. Furthermore\, we show that some complete tripartite graphs\, e.g.\ , the octahedron graph $K_{2\,2\,2}$\, are common and conjecture that ever y complete tripartite graph is common.\n\nJoint work with Andrzej Grzesik\ , Bernard Lidický\, and Jan Volec.\n LOCATION:https://researchseminars.org/talk/EPC/8/ END:VEVENT END:VCALENDAR