MATH 450 Lecture Notes - Lecture 6: Graph Theory, Bipartite Graph, Separating Set
Document Summary
Lecture 6: matching, marriage and menger"s theorem. A complete matching from v1 to v2 in a bipartite graph g(v1, v2) is a one-to-one correspondence between the vertices in v1 and some of the vertices of v2, such that corresponding vertices are joint. Let g(v1, v2) is a bipartite graph, and for each subset a of v1 let (a) be the set of vertices of v2 that are adjacent to at least one vertex of a. V1 to v2 exists ) if and only if |a| | (a)| for each subset a of v1. Two paths from v to w, where that have no edges in common are called edge- disjoint paths. Two paths from v to w, where that have no vertices in common are called vertex-disjoint paths. Let a vw-disconnecting set of g is a set d of edges of g such that each path from v to w includes an edge of d.