A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs
Abstract
We show that the number of k-matching in a given undirected graph G is equal to the number of perfect matching of the corresponding graph Gk on an even number of vertices divided by a suitable factor. If G is bipartite then one can construct a bipartite Gk. For bipartite graphs this result implies that the number of k-matching has a polynomial-time approximation algorithm. The above results are extended to permanents and hafnians of corresponding matrices.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.