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On the minor-minimal 2-connected graphs having a fixed minor |
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| Authors: | Manoel Lemos and James Oxley |
| Institution: | a Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Pernambuco 50740-540, Brazil b Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, USA |
| Abstract: | Let H be a graph with κ1 components and κ2 blocks, and let G be a minor-minimal 2-connected graph having H as a minor. This paper proves that |E(G)|−|E(H)|  (κ1−1)+β(κ2−1) for all (,β) such that +β 5,2+5β20, and β3. Moreover, if one of the last three inequalities fails, then there are graphs G and H for which the first inequality fails. |
| Keywords: | Author Keywords: 2-Connected graph Graph minor Block |
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