Colloquium - Dept of Mathematics and Statistics

Integer flow of 3-edge colorable cubic signed graphs

Rong Luo

West Virginia University

Abstract: Bouchet conjectured in 1983 that every flow-admissible signed graph admits a nowhere-zero 6-flow which is equivalent to the restriction to cubic signed graphs.   Recently we proved that every flow-admissible 3-edge-colorable cubic signed graph admits a nowhere-zero 10-flow.  This together with the 4-color theorem implies that every flow-admissible bridgeless planar signed graph admits a nowhere-zero 10-flow. As a byproduct, we also show that every flow-admissible hamiltonian signed graph admits a nowhere-zero 8-flow. 

This is joint work with C. Li, LC Li, C.-Q Zhang, HL Zhang

Bio: Rong Luo is a professor at the school of Mathematical and Data Science at West Virginia University. His research interests include graph colorings, flows and cycle cover.