, Volume 1, Issue 1, pp 75–78 | Cite as

Recognizing graphic matroids

  • P. D. Seymour


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 35 68 C 25 


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  1. [1]
    R. E. Bixby andW. H. Cunningham, Converting linear programs to network problems,Math. Operations Res., to appear.Google Scholar
  2. [2]
    D. A. Higgs, Strong maps of geometries,J. Combinatorial Theory 5 (1968), 185–191.MATHMathSciNetGoogle Scholar
  3. [3]
    P. M. Jensen andB. Korte, Complexity of matroid property algorithms,Univ. of Bonn Tech. Report No. 78124-0RGoogle Scholar
  4. [4]
    L. Lovász, The matroid matching problem, inAlgebraic Methods in Graph Theory, Proc. Coll. Math. Soc. J. Bolyai, North-Holland 1980.Google Scholar
  5. [5]
    G. C. Robinson andD. J. A. Welsh, The computational complexity of matroid properties,to appear.Google Scholar
  6. [6]
    W. T. Tutte, An algorithm for determining whether a given binary matroid is graphic,Proc. Amer. Math. Soc. 11 (1960), 905–917.CrossRefMathSciNetGoogle Scholar
  7. [7]
    D. J. A. Welsh,Matroid Theory, London Math. Soc. Monograph 8, Academic Press, 1976.Google Scholar

Copyright information

© Akadémiai Kiadó 1981

Authors and Affiliations

  • P. D. Seymour
    • 1
    • 2
  1. 1.Merton CollegeOxfordEngland
  2. 2.University of WaterlooWaterlooCanada

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