Graphs for n-circular matroids

• Autorzy: Renata Kawa
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

matroid   matroidal family  

Kategorie tematyczne

• 05B35: Matroids, geometric lattices
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 3
• Strony: 437-447

Daty

wydano

2010

otrzymano

2009-07-16

poprawiono

2009-08-24

zaakceptowano

2009-09-01

Twórcy

autor

Renata Kawa

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] H. Whitney, On the abstract properties of linear dependence, Amer. J. Math. 57 (1935) 509-533, doi: 10.2307/2371182.
• [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.
• [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.
• [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.
• [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.
• [8] J.L. Gross and J. Yellen, Handbook of Graph Theory (CRC Press, 2004).

Identyfikatory

DOI

10.7151/dmgt.1505