Seminar: Jaeger’s Conjecture is Asymptomatically Almost Surely True for p=2

Speaker: Reaz Huq, TMU

Title: Jaeger’s Conjecture is Asymptomatically Almost Surely True for p=2

Abstract: In 1972, Tutte conjectured that every 4-edge-connected graph has a nowhere-zero flow. It was demonstrated that this is equivalent to every 5-regular, 4-edge-connected graph having an orientation such that every in-degree is either 1 or 4.  In 1988, Jaeger conjectured that every 4p-edge-connected graph has a mod 2p+1 orientation, thereby generalizing Tutte’s conjecture. Jaeger’s conjecture is equivalent to the statement that every 4p+1-regular graph admits a mod 2p+1 orientation.

In this talk, we show that Jaeger’s conjecture is a.a.s. true for p=2 by utilizing the pairing model to demonstrate that a randomly generated 9-regular graph a.a.s. admits a mod 2p+1 orientation. These results make use of the small subgraph conditioning method. 

Joint work with Michelle Delcourt (Toronto Metropolitan University), Pawel Pralat (Toronto Metropolitan University).