×

Bicircular signed-graphic matroids. (English) Zbl 1288.05035

Summary: A theorem of L. R. Matthews [Q. J. Math., Oxf. II. Ser. 28, 213–227 (1977; Zbl 0386.05022)] gives a characterization of graphs whose bicircular matroids are graphic. We give a characterization of graphs whose bicircular matroids are signed-graphic.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
05D15 Transversal (matching) theory

Citations:

Zbl 0386.05022

References:

[1] Dowling, T. A., A class of geometric lattices based on finite groups, J. Combinatorial Theory Ser. B, 14, 61-86 (1973) · Zbl 0247.05019
[2] Matthews, L. R., Bicircular matroids, Quart. J. Math. Oxford (2), 28, 213-228 (1977) · Zbl 0386.05022
[4] Mayhew, D.; Whittle, G.; van Zwam, S. H.M., An obstacle to a decomposition theorem for near-regular matroids, SIAM J. Discrete Math., 25, 1, 271-279 (2011) · Zbl 1290.05057
[5] Oxley, J., Matroid theory, (Oxfordkhachatrian Graduate Texts in Mathematics, vol. 21 (2011), Oxford University Press: Oxford University Press Oxford) · Zbl 1254.05002
[6] Piff, M. J.; Welsh, D. J.A., On the vector representation of matroids, J. Lond. Math. Soc. (2), 2, 284-288 (1970) · Zbl 0213.29102
[7] Simões-Pereira, J. M.S., On subgraphs as matroid cells, Math. Z., 127, 315-322 (1972) · Zbl 0226.05016
[9] Welsh, D. J.A., Combinatorial problems in matroid theory, (Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969) (1971), Academic Press: Academic Press London), 291-306 · Zbl 0233.05001
[10] Whittle, G., On matroids representable over \(G F(3)\) and other fields, Trans. Amer. Math. Soc., 349, 2, 579-603 (1997) · Zbl 0865.05029
[11] Zaslavsky, T., Signed graphs, Discrete Appl. Math., 5, 2, 248 (1983), (erratum) · Zbl 0503.05060
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.