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







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    $begingroup$


    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







    share|cite|improve this question











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      $begingroup$


      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







      share|cite|improve this question











      $endgroup$




      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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 10 at 14:40







      Faustus

















      asked Jan 10 at 11:48









      FaustusFaustus

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