Discussiones Mathematicae Graph Theory 33(3) (2013)
599-602
DOI: https://doi.org/10.7151/dmgt.1689
Broken Circuits in Matroids---Dohmen's Inductive Proof
Wojciech Kordecki
University of Business in Wrocław | Anna Łyczkowska-Hanćkowiak
Poznań University of Economics |
Abstract
Dohmen [4] gives a simple inductive proof of Whitney's famous broken circuits theorem. We generalise his inductive proof to the case of matroids.
Keywords: matroids, broken circuits, induction
2010 Mathematics Subject Classification: 05C15, 05B35.
References
[1] | T. Brylawski, The broken circuit complex, Trans. Amer. Math. Soc. 234 (1977) 417--433, doi: 10.1090/S0002-9947-1977-0468931-6 . |
[2] | T. Brylawski and J. Oxley, The Tutte polynomials and its applications, in: Matroid Applications, ed(s), N. White Cambridge University Press, 1992) 121--225. |
[3] | K. Dohmen, Some remarks on the sieve formula, the Tutte polynomial and Crapo's beta invariant, Aequationes Math. 60 (2000) 108--115, doi: 10.1007/s000100050139. |
[4] | K. Dohmen, An inductive proof of Whitney?s broken circuit theorem, Disscus. Math. Graph Theory 31 (2011) 509--515, doi: 10.7151/dmgt.1561. |
[5] | A.P. Heron, Matroid polynomials, in: Combinatorics, ed(s), D.J.A. Welsh and D.R. Woodall The Institute of Combinatorics and Its Applications, Southend-On-Sea, 1972) 164--202. |
[6] | J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992). |
Received 18 October 2011
Revised 12 July 2012
Accepted 8 November 2012
Close