Combinatorics and Graph Theory · Problem 4.5.1

Systems of Distinct Representatives — David Guichard

Mathematics — Combinatorics · matchings

Problem

In this bipartite graph, find a maximum matching and a minimum vertex cover using the algorithm of this section. Start with the matching shown in red. w1w2w3w4w5w6w7v1v2v3v4v5v6v7v8\begin{array}{ccccccc} w_1 & w_2 & w_3 & w_4 & w_5 & w_6 & w_7\\ & & & & & &\\ v_1 & v_2 & v_3 & v_4 & v_5 & v_6 & v_7 & v_8 \end{array} (See figure in text for the specific edge set.)

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