## Degree Constrained Subgraphs of Linear Graphs |

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alternating path alternating tree augmenting path bipartite graph cardinality algorithm cardinality UDCS Chapter characterization circuit constraints with equality construction cost plane d-factor degree constrained subgraph degree constraints dual linear programs edge weights edges of G Edmonds efficient algorithm expanded exposed vertices factor problem feasible primal feasible solution graph G grow growth Hungarian tree incidence matrix inner vertex integer program integer solution matching problem max cx subject maximum cardinality matching maximum matching maximum solution MDCS minimum noninteger solutions nonorthogonal number of edges number of vertices odd cycles optimal optimum solution orthogonality conditions outer vertex outermost blossom polyhedron primal and dual Proof S-odd subgraph saturated set of edges set of vertices shown simplex algorithm solution to Ax solved strong augment subsequent trees subset symmetric difference Theorem TRANSFER tree is discarded Tutte UDCS cardinality UDCS problem UDCS solution ULDCS unsaturated unscanned vector weak augment weighted graph