On the fractional intersection number of a graph (Q1808721)

The intersection number of a graph \(G\) is the size of the smallest possible set \(S\) such that the vertices of \(G\) are represented by subsets of \(S\) with edges corresponding to intersecting subsets. The intersection number can be determined as the solution to a minimization integer program, and the fractional intersection number is defined as the solution to the linear program relaxation of this integer program. Intersection numbers and fractional intersection numbers are considered for chordal graphs, interval graphs and random Bernoulli graphs.