Mixing
Orthogonal Hypergraphs
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Two hypergraphs $(V,E_1)$ and $(V,E_2)$ are said to be orthogonal if $E_1$ and $E_2$ are partitions of $V$ and the graph induced by $E_1$ and $E_2$ is acyclic and connected (ACC). Is there any equivalent way to state this? I am new to hypergraphs but I was wondering if there is some equivalent condition (probably involving graph partitions) which doesn't involve the ACC induced graph.
Note that by "graph induced by $E_1$ and $E_2$" I mean a bipartite graph with nodes $E_1uplus E_2$ and $e_1in E_1$ shares an edge with $e_2in E_2$ if $e_1cap e_2neemptyset$.
graph-theory hypergraphs
asked Jan 10 at 11:48
FaustusFaustus
1176
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add a comment |
$begingroup$
Two hypergraphs $(V,E_1)$ and $(V,E_2)$ are said to be orthogonal if $E_1$ and $E_2$ are partitions of $V$ and the graph induced by $E_1$ and $E_2$ is acyclic and connected (ACC). Is there any equivalent way to state this? I am new to hypergraphs but I was wondering if there is some equivalent condition (probably involving graph partitions) which doesn't involve the ACC induced graph.
Note that by "graph induced by $E_1$ and $E_2$" I mean a bipartite graph with nodes $E_1uplus E_2$ and $e_1in E_1$ shares an edge with $e_2in E_2$ if $e_1cap e_2neemptyset$.
graph-theory hypergraphs
asked Jan 10 at 11:48
FaustusFaustus
1176
$endgroup$
add a comment |
$begingroup$
Two hypergraphs $(V,E_1)$ and $(V,E_2)$ are said to be orthogonal if $E_1$ and $E_2$ are partitions of $V$ and the graph induced by $E_1$ and $E_2$ is acyclic and connected (ACC). Is there any equivalent way to state this? I am new to hypergraphs but I was wondering if there is some equivalent condition (probably involving graph partitions) which doesn't involve the ACC induced graph.
Note that by "graph induced by $E_1$ and $E_2$" I mean a bipartite graph with nodes $E_1uplus E_2$ and $e_1in E_1$ shares an edge with $e_2in E_2$ if $e_1cap e_2neemptyset$.
graph-theory hypergraphs
asked Jan 10 at 11:48
FaustusFaustus
1176
$endgroup$
Two hypergraphs $(V,E_1)$ and $(V,E_2)$ are said to be orthogonal if $E_1$ and $E_2$ are partitions of $V$ and the graph induced by $E_1$ and $E_2$ is acyclic and connected (ACC). Is there any equivalent way to state this? I am new to hypergraphs but I was wondering if there is some equivalent condition (probably involving graph partitions) which doesn't involve the ACC induced graph.
Note that by "graph induced by $E_1$ and $E_2$" I mean a bipartite graph with nodes $E_1uplus E_2$ and $e_1in E_1$ shares an edge with $e_2in E_2$ if $e_1cap e_2neemptyset$.
graph-theory hypergraphs
graph-theory hypergraphs
asked Jan 10 at 11:48
FaustusFaustus
1176
asked Jan 10 at 11:48
FaustusFaustus
1176
edited Jan 10 at 14:40
Faustus
asked Jan 10 at 11:48
FaustusFaustus
1176
asked Jan 10 at 11:48
FaustusFaustus
1176
asked Jan 10 at 11:48
FaustusFaustus
1176
1176
add a comment |
add a comment |
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