Minimally 4-restricted edge connected graphs - Kamyab, Khalid; Ghasemi, Mohsen; Varmazyar, Rezvan (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
Suppose that G is minimally 4-restricted edge connected graph without triangle, δ(G) ≥ 2 and α4(G) ≥ 6. Suppose that A is a λ4-atom of G such that for each path of length 3 in A, say P3 = xyz, we have dA(y) − 1 = dA−x,y,z(y), where x ∼ y ∼ z. In this paper, under these assumptions, we show that all atoms of G are trivial.