T. Zamfirescu | Dortmund University of Technology - Technische Universität Dortmund (original) (raw)

Papers by T. Zamfirescu

Rendiconti del Seminario Matematico della Università di Padova, 1971

Mathematics, Dec 26, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Linear & Multilinear Algebra, Jun 1, 1993

ABSTRACT This paper deals with the space π(X,X) of all linear transformations L that leave convex... more ABSTRACT This paper deals with the space π(X,X) of all linear transformations L that leave convex sets invariant; for convex sets X and Y in R d, π(X,Y) = {LLXY}. If (X=Y=)K is a convex body then faces of K invariant under L are determined in case 0 intK. Moreover, invariant supporting hyperplanes of K are determined in case K is a simplex in general position. It is shown that π(P 1,P 2) is polyhedral if P 1 and P 2 are polyhedral. Finally, it is shown that for any polyhedral set P, π(P,P) is a polytope iff P is a polytope with lin P=R d.

Electronic Journal of Graph Theory and Applications, 2014

In this note, we consider triangular, square and hexagonal lattices on the flat Klein bottle, and... more In this note, we consider triangular, square and hexagonal lattices on the flat Klein bottle, and find subgraphs with the property that for any j vertices there exists a longest path (cycle) avoiding all of them. This completes work previously done in other lattices.

Mathematische Zeitschrift, 1967

Israel Journal of Mathematics, 1969

Abstract This paper concerns continuous families of planar curves as introduced by B. Grünbaum. ... more Abstract This paper concerns continuous families of planar curves as introduced by B. Grünbaum. With each such family a double closed curve is associated, having the property that each of its points lies on at most two curves of the family.

Bulletin de la Classe des sciences

J. Univers. Comput. Sci., 2007

In this paper we study connectivity and hamiltonicity properties of the topological grid graphs, ... more In this paper we study connectivity and hamiltonicity properties of the topological grid graphs, which are a natural type of planar graphs associated with finite subgraphs of the usual square lattice graph of the plane. The main results are as follows. The shortness coefficient of the family of all topological grid graphs is at most 16/17. Every 3-connected topological grid graph is hamiltonian.

Rendiconti del Circolo Matematico di Palermo, 1969

Mathematische Zeitschrift, 1997

Journal of Combinatorial Theory, Series B, 1982

Barnette's famous conjecture states that the family, denoted here by .9;, of all those simple 3-d... more Barnette's famous conjecture states that the family, denoted here by .9;, of all those simple 3-dimensional polytopes whose faces are even sided contains only Hamiltonian members. Malkevitch [8] raised the question whether the family 9: of all simple polytopes having only pentagons, decagons, 15gons, etc., as faces contains only Hamiltonian members or not. In order to generalize the preceding problems we consider the class 9", of all (always 3-dimensional) polytopes which are k-gonal modulo n. We say that a polytope is k-gonal mod& n (k < n) if all vertices have the same valency and each of its faces is an m-gon with m = k (mod n). The few regular polytopes are all Hamiltonian. We shall see that, for many values of k and n, the polytopes which are k-gonal modulo n may well be non-Hamiltonian, even if they are assumed to be simple (every vertex is 3-valent). The class of all simple k-gonal (modulo n) polytopes (k < n) will be denoted by 9;. Griinbaum and Walther [7] introduced the following "measure" of how short a longest circuit can be, called the shortness exponent and defined for any family ST of graphs a(F) = ",",$f (log h(G))/log u(G), where v(G) is the number of all vertices of G and h(G) the maximal circuit length in G. We identify polytopes with the graphs of their vertices and edges. The case of those simple polytopes which are k-gonal modulo 3 was treated by Zaks [ 141 and Walther [ 121. They proved that ~(9;

Discrete and Computational Geometry, 2003

Archiv der Mathematik, 1995

Acta Mathematica Hungarica

Periodica Mathematica Hungarica, 2015

This is a survey of results obtained during the last 45 years regarding the intersection behaviou... more This is a survey of results obtained during the last 45 years regarding the intersection behaviour of all longest paths, or all longest cycles, in connected graphs. Planar graphs and graphs of higher connectivity receive special attention. Graphs embeddable in the cubic lattice of arbitrary dimension, and graphs embeddable in the triangular or hexagonal lattice of the plane are also discussed. Results concerning the case when not all, but just some longest paths or cycles are intersected, for example two or three of them, are also reported.