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DTSTART;TZID=UTC:20211201T153000
DTEND;TZID=UTC:20211201T163000
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CREATED:20211128T200242Z
LAST-MODIFIED:20211128T200242Z
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SUMMARY:Atlantic Graph Theory Seminar: James Preen (Cape Breton University)
DESCRIPTION:There are many results about triangles in graphs\, but the property that every edge in a graph is in at least one triangle seems not to have been studied before. The 4-regular case was quickly solved collaboratively following an internet posting and then written about by one author in their blog\, before being published in the Journal of Graph Theory in 2013. \nHowever\, the result that was originally wanted was a characterisation for 5-regular graphs\, and that did not emerge as smoothly. With no solution published several years later\, I started working on it and have submiited my paper resolving it in 2021. In this talk I will outline the background and the ideas used in the proof\, which involves cliques\, multiple edges and a generalisation of the the line graph construction. \nJoin Zoom Meeting: link\nTo view previous slides and talks\, click here.
URL:https://aarms.math.ca/event/atlantic-graph-theory-seminar-james-preen-cape-breton-university/
LOCATION:Zoom seminar
CATEGORIES:AARMS Atlantic Graph Theory Seminar
ORGANIZER;CN="Jason Brown":MAILTO:jason.brown@dal.ca
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DTSTART;TZID=UTC:20211208T153000
DTEND;TZID=UTC:20211208T163000
DTSTAMP:20260616T130042
CREATED:20211206T120336Z
LAST-MODIFIED:20211206T120336Z
UID:6547-1638977400-1638981000@aarms.math.ca
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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