Eulerian Subgraphs and S-connectivity of Graphs

Collapsible graphs are introduced by Caltin to study Eulerian subgraphs, and S-group-connectivity is introduced by Jaeger et al. to study flows of graphs. Lai established a connection of those graph classes by showing that collapsible graphs have S-connectivity for group S of order 4. In a survey paper in 2011, Lai et al. conjectured that this property holds for all finite Abelian groups of size at least 4. We prove this conjecture for all groups of even order vertical bar S vertical bar >= 4 and of large odd order vertical bar S vertical bar >= 53. (C) 2020 Elsevier Inc. All rights reserved.