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SUMMARY:Joonkyung Lee (Universität Hamburg)
DTSTART:20200601T130000Z
DTEND:20200601T140000Z
DTSTAMP:20260404T145133Z
UID:EPC/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/EPC/8
 /">On tripartite common graphs</a>\nby Joonkyung Lee (Universität Hamburg
 ) as part of Extremal and probabilistic combinatorics webinar\n\n\nAbstrac
 t\nA graph $H$ 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 c
 olouring. Burr and Rosta\, extending a famous conjecture by Erdős\, conje
 ctured that every graph is common\, which was disproved by Thomason and by
  Sidorenko in late 1980s. Collecting new examples for common graphs had no
 t seen much progress since then\, although very recently\, a few more grap
 hs are verified to be common by the flag algebra method or the recent prog
 ress on Sidorenko's conjecture.\n\nOur contribution here is to give a new 
 class of tripartite common graphs. The first example class is so-called tr
 iangle trees\, which generalises two theorems by Sidorenko and hence answe
 rs a question by Jagger\,  Šťovíček\, and Thomason from 1996. We also 
 prove that\, somewhat surprisingly\, given any tree T\, there exists a tri
 angle tree 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 th
 at every complete tripartite graph is common.\n\nJoint work with Andrzej G
 rzesik\, Bernard Lidický\, and Jan Volec.\n
LOCATION:https://stable.researchseminars.org/talk/EPC/8/
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