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Contractions and the Theorem of Menger
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0-chain 2-connected 2-separation adjoining arborescence belongs bicursal block of G bridge called cell-base chain-group chromatic polynomials coefficient common vertices component of G connected graph corresponding cross-cap crosses cubic graph cut-vertex dart deduce define definition deleting denote digraph distinct dual edge of G end-graphs ends Euler characteristic Eulerian path follows from Theorem G is connected graph G graph theory Hamiltonian circuits Hence induced subgraph Let G Let H link of G link-graph loop Menger's Theorem Moreover nonnull null null graph number of edges orbits oriented outflow path-bundle peripheral circuits permutation Petersen graph planar graphs planar map planar mesh polynomial premap primitive chain Proof proper subgraph residual graphs respectively satisfies spanning subgraph subgraph H subgraph of G subset Suppose tail theorem follows Theorem VII unicursal valency vertex of G vertex-graph vertices of attachment virtual edges W. T. Tutte write zero