query: Number of perfect matchings in a $K_{m,n}$ bipartite graph?
positive_passages.docid: 54749
positive_passages.text: How to find the number of perfect matchings in complete graphs?
negative_passages.docid: 17868
negative_passages.text: How to calculate the number of possible connected simple graphs with $n$ labelled vertices
negative_passages.docid: 45448
negative_passages.text: Minimum number of $k$-partitions of a set of size $n$ to enumerate all $n \choose k$ combinations
negative_passages.docid: 146933
negative_passages.text: Proving bipartition in a connected planar graph
negative_passages.docid: 117862
negative_passages.text: Number of partitions of an $n$-element set into $k$ classes
negative_passages.docid: 89531
negative_passages.text: Show that every graph $G$ has a bipartite subgraph with at least half of the edges of $G$
negative_passages.docid: 62175
negative_passages.text: A general formula for $n$ distinguishable arrangements of length $\ell$ of a sequence of a given size?
negative_passages.docid: 100466
negative_passages.text: The number of labelled graphs with all vertices of even degree
negative_passages.docid: 74730
negative_passages.text: Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
negative_passages.docid: 108631
negative_passages.text: Calulating the Ramsey number $R(T, K_{1,n})$ of a tree $T$ and bipartite graph $K_{1,n}$
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set
negative_passages.docid: 96086
negative_passages.text: Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs
negative_passages.docid: 48692
negative_passages.text: A problem about the graph theory
negative_passages.docid: 26569
negative_passages.text: Counting binary operations on a set with $n$ elements
negative_passages.docid: 89611
negative_passages.text: Combinations of selecting $n$ objects with $k$ different types
negative_passages.docid: 6432
negative_passages.text: How many ways can N elements be partitioned into subsets of size K?
negative_passages.docid: 142861
negative_passages.text: Multipartite graphs which are not planar