Dimension transitiv orientierbarer graphen

Ohne ZusammenfassungDiplomarbeit bei Prof. Dr.E. Specker an der E.T.H. Zürich.     

Kanten-kritische graphen mit der zusammenhangszahl 2

A set of vertices of a graph G represents G if each edge of G is incident with at least one vertex of . A graph G is said to be edge-critical if the minimal number of vertices necessary to represent G decreases if any edge of G is omitted. Plummer [5] has given a method to construct an infinite family of edge-critical graphs with connectivity number 2. We use this method to construct a more extensive class of edge-critical graphs with connectivity number 2 and show that all edge-critical graphs with this connectivity number (K₂) can be constructed from smaller edge-critical graphs. Finally we give examples of edge-critical graphs not constructable from smaller ones by this method.     

Exakte Paare und Kettenkomplexe

It is shown that the category of chain-complexes (of abelian groups) can be embedded as a full reflexive subcategory in the categoryEC of semi-regular exact couples. This situation gives rise to a monad on the categoryEC which has similar properties as the infinite symmetric product [4]. We use this monad and the process of Kan-extensions to study connections between the homology- and homotopyfunctors defined onEC. Furthermore we investigate homotopy-notions inEC and demonstrate that those constructed by W.S. Massey [9] and D.W. Kahn [6] are equivalent.     

Zur bestimmung aller elementarkreise in gerichteten graphen

New algorithms for enumerating all circuits of a directed graph are presented. These algorithms are backtrack algorithms, by which we intended to avoid fruitless computations. The best results give algorithms involving heuristic rules.

To receive numerical comparisons additionally the algorithms of DÖRFLER/MÜHL-BACHER, TIERNAN/SYSLO and BJELKINA were programmed and tested in FORTRAN (CDC 3300) and (or) ALGOL (ICL 4130).     

Exakte SchÄtzer und Konsistente SchÄtzerfolgen

Summary The paper deals with estimates of probability measures (=p-measures) determined from a countable number of independent realizations in a complete separable metric space X. Using an idea of Doob it is shown that the martingale method is applicable for suitable subfamilies , the set of all p-measures on the Borel subsets of X, to establish a correspondence between exact estimates a. e. for and a sequence of estimates which is strongly consistent a. e. for with respect to an arbitrary prior p-measure.     

Eine Min-Max Beziehung für das Exakte Matroid Problem

Ohne ZusammenfassungHerrn Professor Pickert zum 70. Geburtstag gewidmet     

Effiziente,optimale effiziente wege in graphen and diskret-differentielle prozesse mit vektorwertigem funktional

At first discrete-differential processes are reduced to “shortest-path-problems” in graphs without approximation. For vector minimum problems, especially shortest-path-problems with vector-valued lengths of arcs, the notion of an optimal-efficient solution,. of an optimal-efficient path resp. with regard to a real-valued valuation is introduced. To compute an optimal-efficient path, analog of the algorithms of Bellman, Ford, Floyd and Dantzing for vector-valued lengths of arcs and generalized measures of paths are given.