Date : May 11, 2023, 1:30 p.m. - Room :Amphi 2 - Pôle commun

Nowhere-zero flows and group-connectivity in signed graphs

Kathryn NURSE, PhD student - Simon Fraser University, Canada

In 1954, Tutte made a conjecture that every graph without a cut-edge has a nowhere-zero 5-flow. A parallel conjecture to this, but for signed graphs is Bouchet’s Conjecture (1983) that every signed graph without the obvious obstruction has a nowhere-zero 6-flow. We prove that Bouchet’s Conjecture holds in the special case of 3-edge-connected graphs when 6 is replaced with 8. The notion of flows in graphs was generalized to group-connectivity by Jaeger, Linial, Payan, and Tarsi (1992); and to group-connectivity in signed graphs by Li, Luo, Ma, and Zhang (2018). We prove that if a signed graph is 3-edge-connected and 2-unbalanced, then it is A-connected for every abelian group A when |A| is at least six but not equal to seven.