All Questions
Tagged with perfect-matchings hypergraph
8 questions
7
votes
2
answers
571
views
Perfect matchings in certain classes of hypergraphs
While doing research I came unto the following problem:
Given a hypergraph $H$ which is $r$-partite, $r$-uniform (each edge contains exactly $r$ vertices), $k$-regular (each vertex is contained in ...
7
votes
1
answer
696
views
Perfect matching in a vertex-transitive hypergraph
In connection with this MO problem, I wonder whether the hypergraph in
question was actually vertex-transitive. And so, as a natural variation (and,
perhaps, a refinement):
If the vertex set of a ...
- 23k
6
votes
1
answer
526
views
Complexity for calculating number of Perfect Matchings in k-regular hypergraph
Let $G(V,E)$ be a unweighted, k-regular hypergraph, with vertices $V=(v_1, ... v_n)$ and edges $E=(e_1, ... e_m)$. The k-regularity leads to $|e_i|=k$ (i.e. every edge contains exactly $k$ vertices).
...
- 155
6
votes
1
answer
230
views
A non-distinct system of representative edges
I have the following problem:
Let $ \mathcal{G} = (G_{i})\_{i} $ be a collection of graphs on the same vertex set. I would like to find a "system of representative edges" $ f : \mathcal{G} \...
- 161
5
votes
0
answers
115
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
3
votes
1
answer
54
views
$1$-factorizability for "complete" finite hypergraphs
Let $H=(V,E)$ be a hypergraph such that $V\neq \varnothing$ and $\varnothing \notin E$. A matching is a subset $M\subseteq E$ such that $m_1\neq m_2 \in M$ implies $m_1\cap m_2 = \varnothing$, and $M$ ...
- 48.9k
3
votes
0
answers
88
views
Perfect Matching for Edge-transitive Hypergraphs
I'm new to this subject, but I've noticed that a lot of work has been done on perfect matching in k-uniform hypergraphs. I'm curious to know if there are any results on perfect matching in the more ...
- 31
1
vote
0
answers
63
views
$1$-factorizability for linear hypergraphs with infinite edges on $\omega$
Let $H=(V,E)$ be a hypergraph. We say that $M\subseteq E$ is a matching if the members of $M$ are pairwise disjoint, and $M$ is said to be perfect if $\bigcup M = E$. Moreover, $H$ is $1$-factorizable ...
- 48.9k