2023/06/07 by Castano, Alejandra Brewer, McDonald, Jessica, Nurse, Kathryn · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.04151
Jaeger, Linial, Payan, and Tarsi introduced the notion of A-connectivity for graphs in 1992, and proved a decomposition for cubic graphs from which A-connectivity follows for all 3-edge-connected graphs when |A|≥ 6. The concept of A-connectivity was generalized to signed graphs by Li, Luo, Ma, and Zhang in 2018 and they proved that all 4-edge-connected flow-admissible signed graphs are A-connected when |A|≥ 4 and |A|≠ 5. We prove that all 3-edge-connected flow-admissible signed graphs are A-connected when |A|≥ 6 and |A|≠ 7. Our proof is based on a decomposition that is a signed-graph analogue of the decomposition found by Jaeger et. al, and which may be of independent interest.