There is no polynomially bounded algorithm to test if a matroid (presented by an "independence oracle") is binary. However, there is one to test graphicness. Finding this extends work of previous authors, who have given algorithms to test binary matroids for graphicness. Our main tool is a new result that if M′ is the polygon matroid of a graph G, and M is a different matroid on E(G) with the same rank, then there is a vertex of G whose star is not a cocircuit of M.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Computational Mathematics
- AMS subject classification (1980): 05B35, 68C25