What is a relation $R$ called for which $forall x,y,z: neg (x R y wedge y R z)$?

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For a project, I am working with relations $R$ with the property:



$negexists x,y,z: x R y wedge y R z$



Does this property have a name? If so, what is it?




relations




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  • 2




    These sorts of relations can be described as a bipartite graph in which all edges are directed from the same half of the graph to the other: en.wikipedia.org/wiki/Bipartite_graph
    – Connor Harris
    Aug 27 at 14:55






  • 1




    Alternatively (and still in graph theory land), your relation is a (directed) matching.
    – Arthur
    Aug 27 at 14:56










  • (Directed) matching is the kind of answer I'm looking for, thank you.
    – reinierpost
    Aug 27 at 15:07















up vote
0
down vote

favorite












For a project, I am working with relations $R$ with the property:



$negexists x,y,z: x R y wedge y R z$



Does this property have a name? If so, what is it?




relations




share|cite|improve this question
















  • 2




    These sorts of relations can be described as a bipartite graph in which all edges are directed from the same half of the graph to the other: en.wikipedia.org/wiki/Bipartite_graph
    – Connor Harris
    Aug 27 at 14:55






  • 1




    Alternatively (and still in graph theory land), your relation is a (directed) matching.
    – Arthur
    Aug 27 at 14:56










  • (Directed) matching is the kind of answer I'm looking for, thank you.
    – reinierpost
    Aug 27 at 15:07













up vote
0
down vote

favorite









up vote
0
down vote

favorite











For a project, I am working with relations $R$ with the property:



$negexists x,y,z: x R y wedge y R z$



Does this property have a name? If so, what is it?




relations




share|cite|improve this question












For a project, I am working with relations $R$ with the property:



$negexists x,y,z: x R y wedge y R z$



Does this property have a name? If so, what is it?





relations





share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Aug 27 at 14:49









reinierpost

20119




20119







  • 2




    These sorts of relations can be described as a bipartite graph in which all edges are directed from the same half of the graph to the other: en.wikipedia.org/wiki/Bipartite_graph
    – Connor Harris
    Aug 27 at 14:55






  • 1




    Alternatively (and still in graph theory land), your relation is a (directed) matching.
    – Arthur
    Aug 27 at 14:56










  • (Directed) matching is the kind of answer I'm looking for, thank you.
    – reinierpost
    Aug 27 at 15:07













  • 2




    These sorts of relations can be described as a bipartite graph in which all edges are directed from the same half of the graph to the other: en.wikipedia.org/wiki/Bipartite_graph
    – Connor Harris
    Aug 27 at 14:55






  • 1




    Alternatively (and still in graph theory land), your relation is a (directed) matching.
    – Arthur
    Aug 27 at 14:56










  • (Directed) matching is the kind of answer I'm looking for, thank you.
    – reinierpost
    Aug 27 at 15:07








2




2




These sorts of relations can be described as a bipartite graph in which all edges are directed from the same half of the graph to the other: en.wikipedia.org/wiki/Bipartite_graph
– Connor Harris
Aug 27 at 14:55




These sorts of relations can be described as a bipartite graph in which all edges are directed from the same half of the graph to the other: en.wikipedia.org/wiki/Bipartite_graph
– Connor Harris
Aug 27 at 14:55




1




1




Alternatively (and still in graph theory land), your relation is a (directed) matching.
– Arthur
Aug 27 at 14:56




Alternatively (and still in graph theory land), your relation is a (directed) matching.
– Arthur
Aug 27 at 14:56












(Directed) matching is the kind of answer I'm looking for, thank you.
– reinierpost
Aug 27 at 15:07





(Directed) matching is the kind of answer I'm looking for, thank you.
– reinierpost
Aug 27 at 15:07











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For posets this property is called having height $2$.




The height of a poset is the maximum cardinality of a totally-ordered subset.







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  • I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
    – Arthur
    Aug 27 at 15:03











  • Shouldn't it be: having height at most 2?
    – reinierpost
    Aug 27 at 15:09










  • Yep! Corrected.
    – Daron
    Aug 27 at 15:14










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up vote
2
down vote













For posets this property is called having height $2$.




The height of a poset is the maximum cardinality of a totally-ordered subset.







share|cite|improve this answer






















  • I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
    – Arthur
    Aug 27 at 15:03











  • Shouldn't it be: having height at most 2?
    – reinierpost
    Aug 27 at 15:09










  • Yep! Corrected.
    – Daron
    Aug 27 at 15:14














up vote
2
down vote













For posets this property is called having height $2$.




The height of a poset is the maximum cardinality of a totally-ordered subset.







share|cite|improve this answer






















  • I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
    – Arthur
    Aug 27 at 15:03











  • Shouldn't it be: having height at most 2?
    – reinierpost
    Aug 27 at 15:09










  • Yep! Corrected.
    – Daron
    Aug 27 at 15:14












up vote
2
down vote










up vote
2
down vote









For posets this property is called having height $2$.




The height of a poset is the maximum cardinality of a totally-ordered subset.







share|cite|improve this answer














For posets this property is called having height $2$.




The height of a poset is the maximum cardinality of a totally-ordered subset.








share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Aug 27 at 15:14

























answered Aug 27 at 14:56









Daron

4,87811024




4,87811024











  • I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
    – Arthur
    Aug 27 at 15:03











  • Shouldn't it be: having height at most 2?
    – reinierpost
    Aug 27 at 15:09










  • Yep! Corrected.
    – Daron
    Aug 27 at 15:14
















  • I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
    – Arthur
    Aug 27 at 15:03











  • Shouldn't it be: having height at most 2?
    – reinierpost
    Aug 27 at 15:09










  • Yep! Corrected.
    – Daron
    Aug 27 at 15:14















I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
– Arthur
Aug 27 at 15:03





I like this answer. If you just think of $R$ as $<$ rather than $leq$ (as there is no $x$ with $xRx$), then it does seem like a partial order.
– Arthur
Aug 27 at 15:03













Shouldn't it be: having height at most 2?
– reinierpost
Aug 27 at 15:09




Shouldn't it be: having height at most 2?
– reinierpost
Aug 27 at 15:09












Yep! Corrected.
– Daron
Aug 27 at 15:14




Yep! Corrected.
– Daron
Aug 27 at 15:14

















 

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