# Graphs for n-circular matroids

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 3, page 437-447
- ISSN: 2083-5892

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topRenata Kawa. "Graphs for n-circular matroids." Discussiones Mathematicae Graph Theory 30.3 (2010): 437-447. <http://eudml.org/doc/270861>.

@article{RenataKawa2010,

abstract = {We give "if and only if" characterization of graphs with the following property: given n ≥ 3, edges of such graphs form matroids with circuits from the collection of all graphs with n fundamental cycles. In this way we refer to the notion of matroidal family defined by Simões-Pereira [2].},

author = {Renata Kawa},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {matroid; matroidal family},

language = {eng},

number = {3},

pages = {437-447},

title = {Graphs for n-circular matroids},

url = {http://eudml.org/doc/270861},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Renata Kawa

TI - Graphs for n-circular matroids

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 3

SP - 437

EP - 447

AB - We give "if and only if" characterization of graphs with the following property: given n ≥ 3, edges of such graphs form matroids with circuits from the collection of all graphs with n fundamental cycles. In this way we refer to the notion of matroidal family defined by Simões-Pereira [2].

LA - eng

KW - matroid; matroidal family

UR - http://eudml.org/doc/270861

ER -

## References

top- [1] H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57 (1935) 509-533, doi: 10.2307/2371182. Zbl0012.00404
- [2] J.M.S. Simões-Pereira, On matroids on edge sets of graphs with connected subgraphs as circuits II, Discrete Math. 12 (1975) 55-78, doi: 10.1016/0012-365X(75)90095-3. Zbl0307.05129
- [3] J.M.S. Simões-Pereira, Matroidal Families of Graphs, in: N. White (ed.) Matroid Applications (Cambridge University Press, 1992), doi: 10.1017/CBO9780511662041.005. Zbl0768.05024
- [4] J.G. Oxley, Matroid Theory (Oxford University Press, 1992).
- [5] L.R. Matthews, Bicircular matroids, Quart. J. Math. Oxford 28 (1977) 213-228, doi: 10.1093/qmath/28.2.213.
- [6] T. Andreae, Matroidal families of finite connected nonhomeomorphic graphs exist, J. Graph Theory 2 (1978) 149-153, doi: 10.1002/jgt.3190020208. Zbl0347.05119
- [7] R. Schmidt, On the existence of uncountably many matroidal families, Discrete Math. 27 (1979) 93-97, doi: 10.1016/0012-365X(79)90072-4. Zbl0427.05024
- [8] J.L. Gross and J. Yellen, Handbook of Graph Theory (CRC Press, 2004). Zbl1036.05001

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