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47 views

Connected hypergraphs

We say that a hypergraph $H=(V,E)$ is connected if the following condition holds: for all $S\subseteq V$ with $\emptyset\neq S \neq V$ there is $e\in E$ that meets both $S$ and $V\setminus S$, i.e. ...
22 views

Definition of k-partite hypergraph

I would like to know the standard definition of k-partite hypergraph. There are two natural generalizations of k-partite graph to k-partite hypergraph: 1. For all edges e, any two vertices in e are ...
39 views

Induced subgraphs of the line graph of a dense linear hypergraph

Given a hypergraph $H=(V,E)$ we associate to it its line graph $L(H)$ given by $V(L(H)) =E$ and $$E(L(H)) = \big\{\{e_1,e_2\}: e_1\neq e_2 \in E \text{ and } e_1\cap e_2 \neq \emptyset \big\}.$$ We ...
59 views

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 ...
49 views

Injective edge choice functions in linear hypergraphs

A linear hypergraph is a hypergraph $H=(V,E)$ such that for $e\in E$ we have $|e|\geq 2$, and if $e\neq e_1\in E$, then $|e\cap e_1| \leq 1$. An injective edge choice function of a linear ...
55 views

Consequences of Ramsey-numbers of hypergraphs

We know that the (2-color) Ramsey-numbers for $3$-uniform hypergraphs are between roughly $2^{n^2}$ and $2^{2^n}$, and the situation is similar to $k$-uniform hypergraphs for every $k\ge 3$. (A recent ...
45 views

Multigraph Factorisation

I have a graph having 6 vertices and its presentation is $E_{12}^4E_{13}^5E_{14}^6E_{24}^9E_{25}^2E_{35}^9E_{36}L_5^4L_6^{14}$. This means that there are $4$ edges connecting the vertices $1$ and $2$, ...
109 views

Does any long path in a planar graph contain one of O(n) k-tuple of vertices?

My question is a bit related to both the container method and shallow cell complexity. Let's start with that the number of length $\ell$ paths (where $\ell$ denotes the number of vertices of the path!)...
161 views

What is a hypergraph minor?

Is there a theory of hypergraph minors? I could only find some attempts to define them at papers/theses, whose main topic was something else. What would be a useful definition? Does the hypergraph ...
175 views

Graphs with minimum degree $\delta(G)\lt\aleph_0$

Let $G=(V,E)$ be a graph with minimum degree $\delta(G)=n\lt\aleph_0$. Does $G$ necessarily have a spanning subgraph $G'=(V,E')$ which also has minimum degree $\delta(G')=n$ and is minimal with that ...
32 views

Hypergraph mapping's projection

I have been struggling quite a while with a question, which I suspect might have a simple answer to: I have a Graph G = (X,E,Ψ) with E (hyperedge) being a family of subsets of X and Ψ being a mapping ...
77 views

Finding a good transversal basis

A hypergraph $H=(V,E)$ consists of an non-empty set $V$ and a collection $E\subseteq {\cal P}(V)\setminus \{\emptyset\}$ of non-empty subsets of $V$. A transversal of $H$ is a set $T\subseteq V$ such ...
31 views

I'm currently developing an algorithm for computing knot coloring invariants and got to the following question: Given a set $S$ and a certain hyper-graph $H \subseteq S^3$, find a decomposition $S = ... 3answers 841 views Does the hypergraph of subgroups determine a group? A hypergraph is a pair$H=(V,E)$where$V\neq \emptyset$is a set and$E\subseteq{\cal P}(V)$is a collection of subsets of$V$. We say two hypergraphs$H_i=(V_i, E_i)$for$i=1,2$are isomorphic if ... 1answer 55 views Standard names of two finitary properties of hypergraphs? Now we are writing a paper on minimal covers and minimal vertex-covers in hypergraphs and would like to know if there are any standard names for the following two (dual) properties of a hypergraph$(V,...

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