1. Point Set
Click and drag points (n=3)
2. Crossing-Free Partition Graph (drag nodes)
Nodes: CFP (k=2), Edges: differ by 1 element
Crossing-Free Partitions: 0
3. Current Partition
Partition 0/0
Graph Properties
Connected Components
0
Maximum Degree
0
Minimum Degree
0
Average Degree
0.0
Clique Number
0
Diameter
0
Adjacency Matrix
No graph to display
How It Works
Crossing-Free Partitions
A partition is "crossing-free" if the convex hulls of its parts do not intersect.
- Convex hulls are shown as polygons around each part
- If two polygons overlap, the partition is NOT valid
- Drag points to change valid partitions
CFP Graph
Each node represents a crossing-free partition. There is an edge between two nodes if their partitions:
- Have the same number of parts
- Are identical except for one single element
- Would be identical if that element were removed
You can drag the graph nodes! This allows you to reorganize the visualization for better clarity.
Graph Properties
- Connected Components: Number of disconnected subgraphs
- Maximum/Minimum Degree: Highest/lowest number of edges connected to a node
- Average Degree: Average number of edges per node
- Clique Number: Size of the largest complete subgraph
- Diameter: Longest shortest path between any two nodes
- Adjacency Matrix: Matrix representation of graph connections
Export to PDF
The "Save PDF with Graphs" button generates a document that includes:
- Configuration information (n, k)
- Coordinates of all points
- Numbered list of all valid partitions
- Graphs of all valid partitions (6 per page)
- Graph properties and adjacency matrix
- Graph connections
Algorithm
The system generates all possible partitions using a recursive algorithm, then filters those whose convex hulls do not intersect, and finally builds a graph of connections between similar partitions.
Note: For large values of n and k, calculations may take time due to the large number of possible partitions. Starting with small values is recommended.