An Upper Bound on the Number of Edges of a 2-Connected Graph

Let G be a loopless 2-connected graph whose largest cycle has c edges, and whose largest bond has c* edges. We show that |E(G)| ≤ hcc*.

[1]  Terry A. McKee.  Series-parallel graphs: A logical approach , 1983, J. Graph Theory.

[2]  Talmage James Reid,et al.  Ramsey Numbers for Matroids , 1997, Eur. J. Comb..

[3]  W. T. Tutte.  Connectivity in Matroids , 1966, Canadian Journal of Mathematics.

[4]  John Adrian Bondy,et al.  Large cycles in graphs , 1971, Discret. Math..