Avohou, Rémi Cocou; Servatius, Brigitte; Servatius, Herman Maps and \(\Delta \)-matroids revisited. (English) Zbl 1454.05021 Art Discrete Appl. Math. 4, No. 1, Paper No. P1.03, 8 p. (2021). Summary: Using Tutte’s combinatorial definition of a map we define a \(\Delta\)-matroid purely combinatorially and show that it is identical to Bouchet’s topological definition. MSC: 05B35 Combinatorial aspects of matroids and geometric lattices 05C10 Planar graphs; geometric and topological aspects of graph theory 52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) Keywords:matroid; \(\Delta\)-matroid; cellular map; topological surface PDFBibTeX XMLCite \textit{R. C. Avohou} et al., Art Discrete Appl. Math. 4, No. 1, Paper No. P1.03, 8 p. (2021; Zbl 1454.05021) Full Text: DOI arXiv References: [1] A. Bouchet, Greedy algorithm and symmetric matroids,Math. Programming38(1987), 147- 159, doi:10.1007/BF02604639. · Zbl 0633.90089 [2] A. Bouchet, Maps and4-matroids,Discrete Math.78(1989), 59-71, doi:10.1016/ 0012-365X(89)90161-1. [3] C. Godsil and G. Royle,Algebraic Graph Theory, Graduate Texts in Mathematics, Springer New York, 2001,https://books.google.com.au/books?id=pYfJe-ZVUyAC. · Zbl 0968.05002 [4] T. Pisanski and B. Servatius,Configurations from a graphical viewpoint, Birkh¨auser Advanced Texts: Basler Lehrb¨ucher. [Birkh¨auser Advanced Texts: Basel Textbooks], Birkh¨auser/Springer, New York, 2013, doi:10.1007/978-0-8176-8364-1. · Zbl 1277.05001 [5] W. T. Tutte, What is a map?, in:New directions in the theory of graphs (Proc. Third Ann Arbor Conf., Univ. Michigan, Ann Arbor, Mich., 1971), Academic Press, New York, pp. 309-325, 1973. · Zbl 0258.05105 [6] H. Whitney, Congruent Graphs and the Connectivity of Graphs,Amer. J. Math.54(1932), 150- 168, doi:10.2307/2371086 · JFM 58.0609.01 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.