Broken Circuits in Matroids-Dohmen’s Inductive Proof

• Autorzy: Wojciech Kordecki , Anna Łyczkowska-Hanćkowiak
• Języki publikacji: EN

Abstrakty

EN

Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids

Słowa kluczowe

EN

matroids; broken circuits; induction

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 3
• Strony: 599-602

Daty

wydano

2013-07-01

online

2013-07-30

Twórcy

autor

Wojciech Kordecki

• University of Business in Wrocław Department of Management ul. Ostrowskiego 22, 53-238 Wrocław, Poland

autor

Anna Łyczkowska-Hanćkowiak

• Poznań University of Economics Faculty of Informatics and Electronic Economy Department of Operations Research al. Niepodlegości 10, 61-875 Poznań, Poland

Bibliografia

• [1] T. Brylawski, The broken circuit complex , Trans. Amer. Math. Soc. 234 (1977) 417-433. doi:10.1090/S0002-9947-1977-0468931-6[Crossref]
• [2] T. Brylawski and J. Oxley, The Tutte polynomials and its applications, in: Matroid Applications, N. White (Ed(s)), (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[Crossref]
• [4] K. Dohmen, An inductive proof of Whitneys broken circuit theorem, Disscus. Math. Graph Theory 31 (2011) 509-515. doi:10.7151/dmgt.1561[Crossref]
• [5] A.P. Heron, Matroid polynomials, in: Combinatorics, D.J.A. Welsh and D.R. Woodall (Ed(s)), (The Institute of Combinatorics and Its Applications, Southend-On-Sea, 1972) 164-202.
• [6] J.G. Oxley, Matroid Theory (Oxford University Press, Oxford, 1992).

Identyfikatory

DOI

10.7151/dmgt.1689