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Boxicity

In the mathematical field of graph theory, the boxicity of a graph is a graph invariant defined to be the minimum dimension of Euclidean space required to represent the graph as an intersection graph of axis-parallel closed boxes. That is, there must exist a one-to-one correspondence between the vertices of the graph and these boxes, such that two boxes…

Relation to certain graph classes, Algorithmic results & Bounds

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Examples

Relation to certain graph classes

Algorithmic results

Bounds

Related graph invariants

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Boxicity

Nodes46
Edges45
Triples18
Avg. degree1.96
Density0.043478
Components1

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Boxicity

Top relations

related to Algorithmic results · 8
Boxicity → Chandran, Despite, For, Francis, However, Many, NP-complete, Sivadasan
related to Relation to certain graph classes · 4
Boxicity → Because, Roberts, This, Turán
related to Examples · 3
Boxicity → Euclidean, The, This
related to Related graph invariants · 2
Boxicity → Cubicity, Sphericity
is a · 1
Boxicity → generalization of cubicity.Sphericity is defined in the same way as boxicity but with congruent spheres

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Important terminology

graph boxes dimension vertices intersection box two representation graphs displaystyle operatorname defined axis-parallel represented one complete log roberts number 2n

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Boxicityis ageneralization of cubicity.Sphericity is defined in the same way as boxicity but with congruent spheres0.90text
Boxicityrelated to Algorithmic resultsMany0.60section
Boxicityrelated to Algorithmic resultsFor0.60section
Boxicityrelated to Algorithmic resultsHowever0.60section
Boxicityrelated to Algorithmic resultsNP-complete0.60section
Boxicityrelated to Algorithmic resultsChandran0.60section
Boxicityrelated to Algorithmic resultsFrancis0.60section
Boxicityrelated to Algorithmic resultsSivadasan0.60section
Boxicityrelated to Algorithmic resultsDespite0.60section
Boxicityrelated to ExamplesThe0.60section
Boxicityrelated to ExamplesEuclidean0.60section
Boxicityrelated to ExamplesThis0.60section

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