Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
Speaker: | Bruce Richter |
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Affiliation: | University of Waterloo |
Room: | Mathematics and Computer Building (MC) 5158 |
Tutte's 3-flow conjecture asserts that every graph with no 1- or 3-edge-cut has an orientation so that, at every vertex, the number of arcs pointing in is the same (modulo 3) as the number of arcs pointing out. It is known that it suffices to prove that every 5-edge-connected graph has such an orientation.
Recently, Thomassen made a breakthrough, proving this for 8-edge-connected graphs. There is now a very simple proof that it holds for 6-edge-connected graphs. Indeed, this is proved by showing that, modulo 3, prescribing the individual out-degrees at every vertex (to sum to |E(G)| modulo 3) is achievable in 6-edge-connected graphs.
With Thomassen and Younger, we proved that this stronger result also holds for 5-edge-connected planar graphs. Both proofs will be outlined in this talk.
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.