We give a program to rule out some large classes of graphs which cannot be the counter examples for the Krenn-Gu conjecture.
From prior work, it is known that counter example cannot be a Type-2 graph [CG 22]. We roughly implement the Type-2 graph detection algorithm from [CG 22] to detect such graphs. We also detect 2-connected graphs, which can not be a counter example and 3-connected graphs which can not be a minimal counter example.
The graph G is provided input to the program in the following format:
Number of vertices in the graph: <insert |V| here>
Number of edges in the graph: <insert |E| here>
Edges of the graph (1-indexed): <insert all unordered pairs (u,v) in E here>
Plese check Sample Testcases to gain a better understanding of the input / output format.
To run the program, please use Python3.
The command to run the program is:
python "detecting_quantum_graphs.py".
[CG 22] L. S. Chandran and R. Gajjala. Perfect matchings and quantum physics: Progress on Krenn’s Conjecture, 2022.