zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Configurations and graphs. II. (English) Zbl 0868.05049
The aim of this paper is to give a second survey on relations between graphs and configurations in the sense of the author’s first part [Discrete Math. 111, 269-276 (1993; Zbl 0786.05088)]. It contains some further relations as well as additional remarks to topics which were mentioned in the first survey. In particular, a new and quite general connection concerning the existence of certain configurations and the blocking set property is described. The last section contains some historical facts and some general background of the history of configurations.

05C99Graph theory
05B30Other designs, configurations
Full Text: DOI
[1] Barrau, J. A.: Bijdragen tot de theorie der configuraties. Dissertation, Amsterdam (1907) · Zbl 38.0516.03
[2] Barrau, J. A.: Over drietalstelsels, in het bijzonder die Van dertien elementen. Verslag Van de gewone vergaderingen der wis- en natuurkundige afdeeling 17, 274-279 (1908) · Zbl 39.0282.01
[3] Barrau, J. A.: Over de combinatorische opgave Van Steiner. Verslag Van de gewone vergaderingen der wis- en natuurkundige afdeeling 17, 318-326 (1908) · Zbl 39.0281.03
[4] Dorwart, H. L.; Grünbaum, B.: Are these figures oxymora?. Math. mag. 65, 158-169 (1992) · Zbl 0781.05010
[5] Gropp, H.: Configurations and the tutte conjecture. Ars combin. 29A, 171-177 (1990) · Zbl 0739.05016
[6] Gropp, H.: A.díezj.echeverríaa.ibarra on the history of configurations. On the history of configurations, 263-268 (1990)
[7] Gropp, H.: The history of Steiner systems $S(2,3,13)$. Mitteilungen math. Ges. Hamburg 12, 849-861 (1991) · Zbl 0767.05028
[8] Gropp, H.: Enumeration of regular graphs 100 years ago. Discrete math. 101, 73-85 (1992) · Zbl 0759.05052
[9] Gropp, H.: The construction of all configurations (124,163). Ann. discrete math. 51, 85-91 (1992) · Zbl 0767.05035
[10] Gropp, H.: Configurations and graphs. Discrete math. 111, 269-276 (1993) · Zbl 0786.05088
[11] Gropp, H.: Configurations and (r,1)-designs. Discrete math. 129, 113-137 (1994) · Zbl 0801.05017
[12] Gropp, H.: Graph-like combinatorial structures in (r,1)-designs. Discrete math. 134, 65-73 (1994) · Zbl 0808.05027
[13] H. Gropp, Blocking set free configurations and their relations to digraphs and hypergraphs, Discrete Math., to appear. · Zbl 0891.05016
[14] H. Gropp, On tactical configurations, regular bipartite graphs, and (v, k, even)-designs, Discrete Math., to appear. · Zbl 0859.05015
[15] H. Gropp, On combinatorial papers of König and Steinitz, Acta Math. Applicanda, submitted. · Zbl 0913.01017
[16] Kramer, E. S.; Magliveras, S. S.; Mathon, R.: The Steiner systems $S(2,4,25)$ with nontrivial automorphism group. Discrete math. 77, 137-157 (1989) · Zbl 0701.05009
[17] Maclane, S.: Some interpretations of abstract linear dependence in terms of projective geometry. Amer. J. Math. 58, 236-240 (1936) · Zbl 0013.19503
[18] Steinitz, E.: Über die construction der configurationen n3. Dissertation breslau (1894) · Zbl 25.0875.03
[19] Steinitz, E.: Über die unmöglichkeit, gewisse configurationen n3 in einem geschlossenen zuge zu durchlaufen. Monatshefte für Mathematik und physik 8, 293-296 (1897) · Zbl 28.0425.02
[20] De Vries, J.: Over vlakke configuraties waarin elk punt met twee lijnen incident is. Afdeeling natuurkunde 6, 382-407 (1889)
[21] De Vries, J.: Sur LES configurations planes dont chaque point supporte deux droites. Rendiconti circolo mat. Palermo 5, 221-226 (1891) · Zbl 23.0560.01