Graphs for n-circular matroids

Renata Kawa

Discussiones Mathematicae Graph Theory (2010)

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

Abstract

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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].

How to cite

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Renata 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

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  1. [1] H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57 (1935) 509-533, doi: 10.2307/2371182. Zbl0012.00404
  2. [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. [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. [4] J.G. Oxley, Matroid Theory (Oxford University Press, 1992). 
  5. [5] L.R. Matthews, Bicircular matroids, Quart. J. Math. Oxford 28 (1977) 213-228, doi: 10.1093/qmath/28.2.213. 
  6. [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. [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. [8] J.L. Gross and J. Yellen, Handbook of Graph Theory (CRC Press, 2004). Zbl1036.05001

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