BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tao Jiang (Miami University) DTSTART:20200924T020000Z DTEND:20200924T030000Z DTSTAMP:20260423T021015Z UID:SCMSComb/12 DESCRIPTION:Title: Linear cycles of given lengths in linear hypergraphs\nby Tao Jiang ( Miami University) as part of SCMS Combinatorics Seminar\n\n\nAbstract\nA w ell-known result of Verstraete states that for each integer k\\geq 2 every graph G with average degree at least 8k contains cycles of k consecutive even lengths\, the shortest of which is at most twice the radius of G.\n\n In this talk\, we extend Verstraete's result for linear cycles in linear r -uniform hypergraphs\, where r\\geq 3.\nWe show that for each k\\geq 2\, t here exist constants c_1\,c_2 depending only on r such that every linear r -graph with average degree at least c_1 k contains linear cycles of k cons ecutive even lengths and every linear r-graph with average degree at c_2k contains linear cycles of k consecutive lengths. For the even consecutive lengths case\, our bound on the shortest cycle length among the cycles obt ained is tight\, which also yields improved upper bound on the linear Tura n number of an even cycle of given length. For the consecutive lengths cas e\, our bound on the shortest cycle length is tight within a constant fact or.\n\nThe talk will focus on the tools used in establishing the results. We think that these tools can find further applications to other extremal problems on cycles in the hypergraph setting.\n\nThis is joint work with J ie Ma and Liana Yepremyan.\n\npassword 061801\n LOCATION:https://researchseminars.org/talk/SCMSComb/12/ END:VEVENT END:VCALENDAR