Long cycles passing through a specified edge in a 3-connected graph
Hikoe Enomoto, Kazuhide Hirohata, Katsuhiro Ota · Journal of Graph Theory · 1997
We prove the following theorem: For a connected noncomplete graph G, let τ(G): = min{dG(u) + dG(v)|dG(u, v) = 2}. Suppose G is a 3-connected noncomplete graph. Then through each edge of G there passes a cycle of length ≥ min{|V(G)|, τ (G) − 1}. © 1997 John Wiley & Sons, Inc.