| Thursday, April 18th, 2013 | 4pm-5pm | Burnside 920 |
It was conjectured by Tutte (1970s) that every 4-edge connected graph admits a nowhere-zero 3-flow. Jaeger, Linial, Payan and Tarsi (1992 JCTB) further conjectured that every 5-edge-connected graph is Z3-connected. A weak version of the 3-flow conjecture was proposed by Jaeger (1979) that there is an integer h such that every h-edge-connected graph admits a nowhere-zero 3-flow. Thomassen (JCTB to appear) recently solved this open problem by proving that every 8-edge-connected graph is Z3-connected and admits a nowhere-zero 3-flow. In this paper, Thomassen's result is further improved that every 6-edge-connected graph is Z3-connected and admits a nowhere-zero 3-flow. Note that it was proved by Kochol (2001 JCTB) that it suffices to prove the 3-flow conjecture for 5-edge-connected graphs. (Joint work with L. M. Lovasz, C. Thomassen, Y. Wu)