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Article

Havel, Václav ; Klouda, Josef
Skeletons in multigraphs. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 34 (1993), issue 4, pp. 689-696
MSC: 05B30, 05C99, 20N05 | MR 1263797 | Zbl 0815.05020
Keywords:
multigraph; submultigraph with saturated vertices; generating vertex set; vertex basis; skeleton
Summary:
Under a multigraph it is meant in this paper a general incidence structure with finitely many points and blocks such that there are at least two blocks through any point and also at least two points on any block. Using submultigraphs with saturated points there are defined generating point sets, point bases and point skeletons. The main result is that the complement to any basis (skeleton) is a skeleton (basis).
References:
[1] Dembowski P.: Finite Geometries. Heidelberg, New York, 1968. MR 0233275 | Zbl 0865.51004
[2] Krapež A., Taylor M.A.: Bases of web configurations. Publ de l'Inst. Math., nouvelle série 38 (52) (1985), 21-30. MR 0837378
[3] Belousov V.D.: Configurations in Algebraic Nets (in Russian). Kishinev, 1979. MR 0544665
[4] Havel V.: Regulated bildups of $3$-configurations. Archivum Mathematicum, 1993, to appear. MR 1282109
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