Let H be a graph with κ1 components and κ 2 blocks, and let G be a minor-minimal 2-connected graph having H as a minor. This paper proves that |E(G)|-|E(H)|≤α(κ 1-1)+β(κ2-1) for all (α,β) such that α+β≥5,2α+5β≥;20, and β≥3. Moreover, if one of the last three inequalities fails, then there are graphs G and H for which the first inequality fails. © 2003 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Lemos, M., & Oxley, J. (2004). On the minor-minimal 2-connected graphs having a fixed minor. Discrete Mathematics, 280 (1-3), 77-118. https://doi.org/10.1016/j.disc.2003.07.003