Linked from

The 13 pages that link to Hall's marriage theorem, each with the reason it gives.

• Bipartite graphRelated: It characterizes when every vertex on one side can receive a distinct partner.

• Matching (graph theory)Related: It gives a precise condition for assigning distinct partners to one whole side.

• Augmenting pathRelated: It characterizes when a complete matching exists, while augmenting paths provide an algorithmic route to one.

• Bipartite matchingRelated: It characterizes when every vertex on one side can be matched.

• Perfect matchingRelated: When the two sides are equal in size, its condition characterizes perfect matchings.

• Menger's theoremRelated: Both theorems express existence of disjoint structures through constraints on separating sets.

• Max-flow min-cut theoremRelated: Its neighborhood condition can be understood through cuts in a matching flow network.

• Kőnig's theoremRelated: Its neighborhood condition is another way to detect whether the matching can be enlarged.

• Blossom algorithmCompared with: Its simpler bipartite setting avoids the odd-cycle obstruction blossoms address.

• Maximum-cardinality matchingRelated: It determines whether every member of one group can be assigned a distinct partner.

• Dinitz theoremRelated: Hall’s condition supplies the matching step used to build the coloring.

• Grimm's conjectureRelated: It supplies a general criterion for whether the required prime choices can be made.

• Tutte's theorem on perfect matchingsCompared with: Hall's neighborhood condition replaces odd-component counting in bipartite graphs.