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# Algebra/Topology Seminar – Elena Pavelescu, University of South Alabama

## October 23, 2017 @ 4:00 pm - 5:00 pm

Title: Complete minors of self-complementary graphs.

Abstract: A self-complementary graph on n vertices is a graph which is isomorphic to its graph complement within K_n, the complete graph on n vertices. These graphs have a high degree of structure, and yet they are far from trivial. This talk focuses on minors of self-complementary graphs. Minors of a graph are obtained through sequences of vertex deletions, edge deletions and edge contractions. We show a self-complementary graph on 4n vertices has the complete graph on 2n vertices as minor. Moreover, a self-complementary graph on 4n + 1 vertices has the complete graph on 2n + 1 vertices as minor. We discuss some topological consequences: (1) self-complementary graphs on at least 9 vertices are not planar (2) self-complementary graphs on at least 12 vertices are intrinsically linked, and (3) self-complementary graphs on at least 13 vertices are intrinsically knotted. This is joint work with Andrei Pavelescu.