Realizing Degree Sequences With S3‐Connected Graphs

A graph is ‐connected if, for any mapping with , there exists a strongly connected orientation satisfying for any . It is known that ‐connected graphs are contractible configurations for the property of flow index strictly less than three. In this paper, we provide a complete characterization of graphic sequences that have an ‐connected realization: A graphic sequence has an ‐connected realization if and only if and . Consequently, every graphic sequence with has a realization with flow index strictly less than three. This supports the conjecture of Li, Thomassen, Wu and Zhang [European J. Combin., 70 (2018) 164‐177] that every 6‐edge‐connected graph has a flow index strictly less than three.