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Partitions and Distances in Graphs
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adjacent algorithm application arc progression associated assume bipartite graph called chain flow chain joining characterization colors column complete graph components connected graph consider contains corresponding defined denote determine directed graph disconnecting set edge progression Electrical Networks elements end points Euler graph Euler's formula example Exercise exists feasible flow Figure finite geometric graph given graph G graph of Fig graph theory hamiltonian circuit hamiltonian path hence incidence matrix initial vertex integer intersections isomorphic Kuratowski labeled least Lemma length linear loops Math matroid maximal matching minimal coverings network flows nonplanar Note number of edges number of vertices obtained oriented pair of vertices partitioning permutation planar graph possible problem proof regions represent rooted tree sequence set of edges shown in Fig simple chain simple circuit simple cycles simple graph strongly connected strongly connected graph subset terminal vertex Theorem tion undirected variables vector zero