randomBinomialEdgeIdeal -- Creates a binomial edge ideal from a random graph with n vertices and t edges.

Synopsis

Usage:

(I,G) = randomBinomialEdgeIdeal(n,t)
Inputs:
- n, an integer, number of vertices
- t, an integer, number of edges
Outputs:
- I, an ideal, a random binomial edge ideal
- G, a graph, the graph underlying I

Description

The binomial edge ideal associated to a graph G is the quadratic binomial ideal generated by the set containing x_v*y_w-x_w-y_v for every edge (v,w) in G. This method returns the binomial edge ideal I of a random graph G which has n vertices and t edges.

i1 : randomBinomialEdgeIdeal(7, 4)

o1 = (ideal (- x y  + x y , - x y  + x y , x y  - x y , x y  - x y ),
                3 4    4 3     3 5    5 3   4 1    1 4   6 7    7 6  
                                                                     
                                                                     
                                                                     
                                                                     
     ------------------------------------------------------------------------
     Graph{"edges" => {{x , x }, {x , x }, {x , x }, {x , x }}})
                         3   4     1   4     6   7     3   5
           "ring" => QQ[x ..x ]
                         1   7
           "vertices" => {x , x , x , x , x , x , x }
                           1   2   3   4   5   6   7

o1 : Sequence

Ways to use randomBinomialEdgeIdeal :

randomBinomialEdgeIdeal(ZZ,ZZ)

For the programmer

The object randomBinomialEdgeIdeal is a method function.

randomBinomialEdgeIdeal -- Creates a binomial edge ideal from a random graph with n vertices and t edges.

Synopsis

Description

See also

Ways to use randomBinomialEdgeIdeal :

For the programmer