Data.Matroid.Graphic

This module provides implementations of graphic matroids.

Documentation

data GraphicMatroid v a

data type representing the cycle matroid (aka. polygon matroid) of a (multi-)graph

Instances

(Ord a, Ord v, Show a) => Matroid (GraphicMatroid v) a

Defined in Data.Matroid.Graphic

Methods

groundset :: GraphicMatroid v a -> Set a

showName :: GraphicMatroid v a -> String

rk :: GraphicMatroid v a -> Set a -> Int

indep :: GraphicMatroid v a -> Set a -> Bool

basis :: GraphicMatroid v a -> Set a -> Set a

cl :: GraphicMatroid v a -> Set a -> Set a

abstract :: GraphicMatroid v a -> AMatroid a

dual :: GraphicMatroid v a -> AMatroid a

restriction :: GraphicMatroid v a -> Set a -> AMatroid a

contraction :: GraphicMatroid v a -> Set a -> AMatroid a

loops :: GraphicMatroid v a -> Set a

coRk :: GraphicMatroid v a -> Set a -> Int

coloops :: GraphicMatroid v a -> Set a

Show a => Show (GraphicMatroid v a)

Defined in Data.Matroid.Graphic

Methods

showsPrec :: Int -> GraphicMatroid v a -> ShowS

show :: GraphicMatroid v a -> String

showList :: [GraphicMatroid v a] -> ShowS

fromGraph

Arguments

:: (Ord a, Show a)

=> Set a

set of edges of the (multi-)graph

-> (a -> (v, v))

map that maps the edge e to the set of its incident vertices {u,v}; the order is ignored, and {v} is represented by (v,v)

-> GraphicMatroid v a

constructs a GraphicMatroid from a set of (abstract) edges and the incident-vertex map

namedFromGraph

Arguments

:: Ord a

=> String

name of the matroid

-> Set a

set of edges of the (multi-)graph

-> (a -> (v, v))

map that maps the edge e to the set of its incident vertices {u,v}; the order is ignored, and {v} is represented by (v,v)

-> GraphicMatroid v a

constructs a named GraphicMatroid from a set of (abstract) edges and the incident-vertex map

fromGraph'

Arguments

:: Ord a

=> Set a

set of edges of the (multi-)graph

-> (a -> (v, v))

map that maps the edge e to the set of its incident vertices {u,v}; the order is ignored, and {v} is represented by (v,v)

-> GraphicMatroid v a

constructs an unnamed GraphicMatroid from a set of (abstract) edges and the incident-vertex map

mK

Arguments

:: Int

n = number of vertices in K_n

-> GraphicMatroid Int (Int, Int)

constructs the graphic matroid M(K_n) where K_n is the complete graph on n vertices