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Results tagged with matching-theory
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user 63938
For questions about matchings in graph theory. A matching on a graph is a set of edges such that no two edges share a common vertex.
4
votes
2
answers
440
views
Graphs with unique 1-Factorization
Let $G(V,E)$ be a graph with a 1-factorizations $M$ and $m=|M|$ 1-factors. I am searching for graphs with unique 1-factorizations (i.e. there is only one 1-factorization).
Examples:
Cyclic graph $C …
- 155
21
votes
2
answers
4k
views
Graphs with only disjoint perfect matchings
Let $G(V,E)$ be a graph. I am searching for graphs with only disjoint perfect matchings (i.e. every edge only appears in at most one of the perfect matchings).
Examples:
Cyclic graph $C_n$ with eve …
- 155
8
votes
1
answer
494
views
Fastest algorithm for counting perfect matchings in a general graph
Let $G(V,E)$ be a undirected graph. I am interested in the fastest known algorithm for counting the number of perfect matchings in $G(V,E)$ (which is known to be in $\#P$). In particular, what is the …
- 155
10
votes
0
answers
741
views
Has this notion of vertex-coloring of graphs been studied?
In a study of a quantum physics problem, I came about an apparently very natural type of vertex colorings of a graph. The colors of the vertex $v_i$ is inherited from perfect matchings $PM$ of an edge …
- 155
5
votes
0
answers
114
views
Hypergraphs with only disjoint perfect matchings
Let $H(n,r)$ be the set of $r$-uniform hypergraph with $n$ vertices that have only disjoint perfect matchings (i.e. every hyperedge only appears in at most one of the perfect matchings). Let $m(h(n,r) …
- 155
11
votes
1
answer
816
views
Graphs with only disjoint perfect matchings, with coloring
The following purely graph-theoretic question is motivated by quantum mechanics.
Definitions: A bi-colored graph $G$ is an undirected graph where every edge is colored. An edge can either be monochro …
- 155