[Nauty] Generate all non-isomorphic factor-critical graphs

[lczhangmath]

Hi
I want to generate all non-isomorphic factor-critical graphs given the number of vertices and edges. For a concrete example, consider factor-critical graphs with 13 vertices, a minimum degree of at least 4, a maximum degree of at most 7, and 43 edges. One approach is to first use nauty to generate candidate graphs and then filter them using a function that checks for the factor-critical property. I am also considering another approach: leveraging Lovász's result on the existence of an odd ear decomposition, which could enable a recursive generation method similar in spirit to nauty. Has any previous work been done in this area?


Licheng