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DTSTART:20210101T000000
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DTSTART;TZID=UTC:20211208T153000
DTEND;TZID=UTC:20211208T163000
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CREATED:20211206T120336Z
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SUMMARY:Atlantic Graph Theory Seminar: Sandra Kingan (Brooklyn College and Graduate Center\, CUNY)
DESCRIPTION:I will begin by giving a general overview of what it means to find monarchs for excluded minor classes of graphs and matroids. In a paper that appeared in 2018\, I used the Strong Splitter Theorem to give a short proof of Oxley’s result that the class of binary matroids with no 4-wheel minor consists of a few small matroids and an infinite family of maximal 3-connected rank r matroids known as the binary spikes. Such a family is called a monarch for the excluded minor class. This proof essentially comes down to finding the monarchs for non-regular matroids with no minors isomorphic to a 9-element rank 4 matroid known as P9 or its dual P*9. In a paper that appeared this year (Australasian Journal of Combinatorics\, 79(3)\, 302–326)\, I was able to strengthen the result by characterizing the class of binary non-regular matroids with no minor isomorphic to just P*9. The only members of this class are the rank 3 and 4 binary projective geometries\, a 16-element rank 5 matroid\, and two monarchs: the rank r binary spikes with 2r+1 elements mentioned earlier and another infinite family with 4r−5 elements. As a consequence\, a simple binary matroid of rank at least 6 with no P*9-minor has size at most r(r+1)/2 and this bound is attained by the rank r complete graph. This is one of few excluded minor classes for which the members are so precisely determined. \n  \nJoin Zoom Meeting: link
URL:https://aarms.math.ca/event/atlantic-graph-theory-seminar-sandra-kingan-brooklyn-college-and-graduate-center-cuny/
LOCATION:Zoom seminar
CATEGORIES:AARMS Atlantic Graph Theory Seminar
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