Math.Combinatorics.Hypergraph

A module defining a type for hypergraphs.

Documentation

data Hypergraph a

Constructors

H [a] [[a]]

Instances

Eq a => Eq (Hypergraph a)

Ord a => Ord (Hypergraph a)

Show a => Show (Hypergraph a)

isUniform :: Ord a => Hypergraph a -> Bool

Is this hypergraph uniform - meaning that all blocks are of the same size

incidenceGraph :: Ord a => Hypergraph a -> Graph (Either a [a])

isPartialLinearSpace :: Ord a => Hypergraph a -> Bool

isProjectivePlane :: Ord a => Hypergraph a -> Bool

Is this hypergraph a projective plane - meaning that any two lines meet in a unique point, and any two points lie on a unique line

isProjectivePlaneTri :: Ord a => Hypergraph a -> Bool

Is this hypergraph a projective plane with a triangle. This is a weak non-degeneracy condition, which eliminates all points on the same line, or all lines through the same point.

isProjectivePlaneQuad :: Ord a => Hypergraph a -> Bool

Is this hypergraph a projective plane with a quadrangle. This is a stronger non-degeneracy condition.

isGeneralizedQuadrangle :: Ord a => Hypergraph a -> Bool

isConfiguration :: Ord a => Hypergraph a -> Bool

Is this hypergraph a (projective) configuration.

fanoPlane :: Hypergraph Integer

heawoodGraph :: Graph (Either Integer [Integer])

The Heawood graph is the incidence graph of the Fano plane

desarguesConfiguration :: Hypergraph [Integer]

desarguesGraph :: Graph (Either [Integer] [[Integer]])

pappusConfiguration :: Hypergraph Integer

pappusGraph :: Graph (Either Integer [Integer])

coxeterGraph :: Graph [Integer]

tutteCoxeterGraph :: Graph (Either [Integer] [[Integer]])

The Tutte-Coxeter graph, also called the Tutte 8-cage