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### What is the recognition complexity of k-uniform k-partite hypergraphs? [duplicate]

We can easily recognize bipartite graphs, but I surprisingly couldn't find anything on the recognition complexity of 3-uniform tripartite hypergraphs, though I'm sure this has been studied. It's also ...
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### Complexity of testing if a hypergraph has generalized hypertreewidth $2$

A hypergraph $H = (V, E)$ consists of a set of vertices $V$ and a set $E$ of hyperedges, i.e., subsets of $V$. The generalized hypertreewidth (GHW) parameter is a measure of the cyclicity of a ...
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### Complexity of #SAT for monotone DNF formulae whose hypergraph is a hypertree

A monotone DNF on variables $x_1, \ldots, x_n$ is a disjunction of clauses, each clause being a conjunction of some of the $x_1, \ldots, x_n$. The #SAT problem asks, given a monotone DNF $\Phi$, how ...
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### Is there an approximation algorithm for MAX k DOUBLE SET COVER?

Given a set system $(X,\mathcal S)$, let us say that a subset $\mathcal C\subseteq \mathcal S$ doubly covers a vertex $x$ in $X$ if $x$ is contained in at least two sets of $\mathcal C$. Let us define ...
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### NP-hardness of coloring uniform hypergraphs

Since a $2$-uniform hypergraphs are just graphs. The problem of deciding if $2$-uniform is $k$-colorable for $k=1,2$ is easy, and NP-hard for $k \geq 3$ colors. This is well know and I have seen ...
508 views

### Hardness of 3-dimensional matching variant

I am thinking about a variant of 3-dimensional matching. In normal 3d matching, we have three sets of vertices $X$, $Y$ and $Z$, and a set of edges $E \subseteq X \times Y \times Z$. We want to choose ...
199 views

### Intersection models for weakly chordal graphs?

Due to the apparent unpopularity of my previous posts, I'd like to post a question about graph theory which seems to be a popular topic here :) Among the many known classes of perfect graphs, there ...
418 views

### Which properties of planar graphs generalize to higher dimension / hypergraphs?

A planar graph is a graph which can be embedded in the plane, without having crossing edges. Let $G=(X,E)$ be a $k$-uniform-hypergraph, i.e. an hypergraph such that all its hyperedges have size k. ...
194 views

### Best approximation for a HYPERGRAPH-MAXDICUT problem

Consider a $(c^a,(c+d)^a,1)$-regular directed hypergraph $\mathcal{H}(a)$ on $n^a$ vertices with fixed $n\geq c+d+1$, fixed $c\geq 2$, fixed $d\geq 0$ and variable parameter $a\geq 1$ (meaning every ...
933 views

### hardness of approximating the chromatic number in graphs with bounded degree

I am looking for hardness results on vertex coloring of graphs with bounded degree. Given a graph $G(V,E)$, we know that for any $\epsilon>0$, it's hard to approximate $\chi(G)$ within a factor ...
3k views

### Recognizing line graphs of hypergraphs

The line graph of a hypergraph $H$ is the (simple) graph $G$ having edges of $H$ as vertices with two edges of $H$ are adjacent in $G$ if they have nonempty intersection. A hypergraph is an $r$-...
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### k-uniform k-partite hypergraph matching in polynomial time

I have what seems like an elementary question, but google didn't throw up any answers for it. I would appreciate any pointers users here may provide. Please note that I have also asked this question ...
572 views

### What are the root difficulties in going from graphs to hypergraphs?

There are many examples in combinatorics and computer science where we can analyze a graph-theoretic problem but for the problem's hypergraph analog, our tools are lacking. Why do you think problems ...
629 views