Degree Sequences, Bisections, and Edge-Disjoint 1-factors
Tyler Seacrest, UNL
Meeting Time: January 18, 2011, 2:00-2:50pm
Abstract:
Kundu's Theorem for degree sequences gives a necessary and sufficient condition for a degree sequence to have a realization that contains a \(k\)-factor. A conjectured generalization of the Kundu result is that the same condition yields \(k\) edge-disjoint \(1\)-factors. To make progress on this conjecture, we search for a substructure called a bisection. This allows us to make progress on finding \(1\)-factors in both the realm of degree sequences, and more generally in the realm of simple graphs.