Broken Circuits in Matroids-Dohmen’s Inductive Proof
Wojciech Kordecki; Anna Łyczkowska-Hanćkowiak
Discussiones Mathematicae Graph Theory (2013)
- Volume: 33, Issue: 3, page 599-602
- ISSN: 2083-5892
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topWojciech Kordecki, and Anna Łyczkowska-Hanćkowiak. "Broken Circuits in Matroids-Dohmen’s Inductive Proof." Discussiones Mathematicae Graph Theory 33.3 (2013): 599-602. <http://eudml.org/doc/268224>.
@article{WojciechKordecki2013,
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},
author = {Wojciech Kordecki, Anna Łyczkowska-Hanćkowiak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {matroids; broken circuits; induction},
language = {eng},
number = {3},
pages = {599-602},
title = {Broken Circuits in Matroids-Dohmen’s Inductive Proof},
url = {http://eudml.org/doc/268224},
volume = {33},
year = {2013},
}
TY - JOUR
AU - Wojciech Kordecki
AU - Anna Łyczkowska-Hanćkowiak
TI - Broken Circuits in Matroids-Dohmen’s Inductive Proof
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 3
SP - 599
EP - 602
AB - Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids
LA - eng
KW - matroids; broken circuits; induction
UR - http://eudml.org/doc/268224
ER -
References
top- [1] T. Brylawski, The broken circuit complex , Trans. Amer. Math. Soc. 234 (1977) 417-433. doi:10.1090/S0002-9947-1977-0468931-6[Crossref] Zbl0368.05022
- [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. Zbl0769.05026
- [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] Zbl0959.05002
- [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).
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