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Order dimension

In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order. Dushnik & Miller (1941) first studied order dimension; for a more detailed…

Art, Order dimension two & Order dimension of incidence posets of graphs

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Order dimension two

Comparability graphComplementPermutation graphsSeries-parallel partial ordersHasse diagrams
6 related topics

Order dimension of incidence posets of graphs

Incidence posetUndirected graphPath graphSchnyder's theoremPlanar graph
6 related topics

Formal definition

Linear extensionsEmbedsComponentwise ordering
3 related topics

Realizers

CardinalityCritical pair
2 related topics

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Formal definition

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Order dimension two

Computational complexity

Order dimension of incidence posets of graphs

K-dimension and 2-dimension

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Order dimension

Nodes36
Edges35
Triples105
Avg. degree1.94
Density0.055556
Components1

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Order dimension

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related to References · 68
Order dimension → Algebraic, American Journal, Baker, Ben, BF00353652, BF00383178, Brightwell, Combinatorics, Computing, Dimension, Discrete Mathematics, Discrete Methods, Dushnik, Eugene, Fishburn, Graham, Hiraguti, Hoşten, ISBN, ISSN
related to Order dimension two · 13
Order dimension → Baker, Cartesian, Fishburn, Hasse, If, Lawler, Roberts, Tarjan, That, The, Therefore, They, Valdes
related to Order dimension of incidence posets of graphs · 9
Order dimension → Certain, For, Hoşten, It, Morris, Schnyder, Schnyder's, The, Theta
related to Order dimension of planar maps · 7
Order dimension → As, Brightwell, It, On, Schnyder's, Thus, Trotter
related to Computational complexity · 4
Order dimension → However, It, NP-complete, Yannakakis
related to Formal definition · 3
Order dimension → In, That, The
is a · 1
Order dimension → minimal number of total orders such that P embeds into their product with componentwise ordering i.e. x

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order dimension displaystyle poset partial orders two incidence doi planar graph 10 intersection linear partially ordered trotter realizer set graphs

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SubjectPredicateObjectConfidenceSrc
Order dimensionis aminimal number of total orders such that P embeds into their product with componentwise ordering i.e. x0.90text
Order dimensionrelated to Computational complexityIt0.60section
Order dimensionrelated to Computational complexityHowever0.60section
Order dimensionrelated to Computational complexityNP-complete0.60section
Order dimensionrelated to Computational complexityYannakakis0.60section
Order dimensionrelated to Formal definitionThe0.60section
Order dimensionrelated to Formal definitionIn0.60section
Order dimensionrelated to Formal definitionThat0.60section
Order dimensionrelated to Order dimension of incidence posets of graphsThe0.60section
Order dimensionrelated to Order dimension of incidence posets of graphsCertain0.60section
Order dimensionrelated to Order dimension of incidence posets of graphsSchnyder's0.60section
Order dimensionrelated to Order dimension of incidence posets of graphsSchnyder0.60section

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