Guichard-Combinatorics-Graph-Theory · Problem 4.5.1

Systems of Distinct Representatives

Mathematics — Probability · matchings

Problem

In the bipartite graph below, find a maximum matching and a minimum vertex cover using the algorithm of this section. Start with the matching shown in red. w1w2w3w4w5w6w7∙∙∙∙∙∙∙\begin{array}{ccccccc} w_1 & w_2 & w_3 & w_4 & w_5 & w_6 & w_7 \\ \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet \end{array} v1v2v3v4v5v6v7v8∙∙∙∙∙∙∙∙\begin{array}{cccccccc} v_1 & v_2 & v_3 & v_4 & v_5 & v_6 & v_7 & v_8 \\ \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet & \bullet \end{array}

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