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k-subset intersection graphs with cardinality restrictions on the intersection of adjacent subsets
- Parameters:
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| groundSetCardinality | The ground set cardinality |
| subsetCardinality | The subset cardinality |
| minimumIntersection | A lower bound on the intersection cardinality of adjacent subsets |
| maximumIntersection | An upper bound on the intersection cardinality of adjacent subsets |
| _CT | The controller object to manage the created graph |
The node set of this graph consists from all subsets of a certain ground set with a given subsetCardinality. Of the ground set, only the groundSetCardinality is specified. Two graph nodes are adjacent if the intersection cardinality of the corresponding subsets is in the range [minimumIntersection,maximumIntersection].
The drawing shows the nodes on concentric circles with node indices increasing from the center point to the exterior circle. The nodes on the k-th circle represent the subset which can be built from the first subsetCardinality + k ground set elements - actually containing the k-th element.
This construction covers several known graph classes:
- Complete graphs, taking
minimumIntersection = maximumIntersection = 0 and subsetCardinality = 1. But prefer denseGraph for its efficent data structures. - Triangular graphs, taking
minimumIntersection = maximumIntersection = 1 and subsetCardinality = 2. But prefer triangularGraph to obtain symmetric drawings. - Kneser graphs, taking
minimumIntersection = maximumIntersection = 0 - Generalized Kneser graphs, taking
minimumIntersection = 0 - Johnson graphs, taking
minimumIntersection = maximumIntersection = subsetCardinality-1
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