, Volume 1, Issue 1, pp 75–78

Recognizing graphic matroids


  • P. D. Seymour
    • Merton College
    • University of Waterloo

DOI: 10.1007/BF02579179

Cite this article as:
Seymour, P.D. Combinatorica (1981) 1: 75. doi:10.1007/BF02579179


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 ifM′ is the polygon matroid of a graphG, andM is a different matroid onE(G) with the same rank, then there is a vertex ofG whose star is not a cocircuit ofM.

AMS subject classification (1980)

05 B 3568 C 25
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© Akadémiai Kiadó 1981