# Questions tagged [hypergraph]

Hypergraphs are generalizations of graphs, where edges can be made of more than two vertices.

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### Edge coloring in dense linear hypergraphs

Let $H=(V,E)$ be a hypergraph. If $\kappa$ is a cardinal, we say that a map $c:E\to \kappa$ is an edge coloring if whenever $e_1,e_2\in E$ with $e_1\cap e_2\neq \emptyset$ then $c(e_1)\neq c(e_2)$. ...
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### Dominating vertex sets in hypergraphs

Let $H=(V,E)$ be a hypergraph such that $\bigcup E = V$. For $D\subseteq V$ we set $N_D = \bigcup\{e\in E: D\cap e\neq \emptyset\}$. We say that $D\subseteq V$ is dominating if $N_D = V$. ...
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### Number of even degree subgraphs with given size in 3-uniform hypergraph clique

3-uniform hypergraph clique is a 3-uniform undirected hypergraph containing all possible hyperedges. Even degree subgraph is a hypergraph in which all vertices have even degree. The size of the ...
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### Independence number of $4$-uniform regular hypergraph

Let $H$ be a $4$-uniform hypergraph on $[1..n]$, i.e. $H$ is a collection of $4$-element subsets of $[1..n]$. The elements of $H$ are called edges. A hypergraph is regular if every element of $[1..n]$ ...
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### Helly vs Strong p-Helly Property of Hypergraphs

I am not clear about the difference between Helly and Strong p-Helly property. For example hypergraph H(V, E), V = { 1,2,3 } and E = {(1,2), (2,3), (1,3)} has non-empty set for each pair of ...
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### Minimizing the set of multiply covered elements in a linear hypergraph

We say that a hypergraph $H=(V,E)$ is a linear hypergraph if it has the following properties: if $e_1\neq e_2\in E$ then $|e_1\cap e_2|\leq 1$, and $\bigcup E = V$. We say that $C\subseteq E$ is a ...
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### Does hereditary 2-coloring imply polychromatic 3-coloring for large edges?

For a hypergraph $\mathcal H=(V,\mathcal E)$, denote by $m_k$ the smallest number for which we can $k$-color any $X\subset V$ such that for any $E\in \mathcal E$ with $|E\cap X|\ge m_k$ all $k$ colors ...