**Seminar on Applied Mathematics**

**PROGRAM**

Matematicki fakultet

Fakultet organizacionih nauka

JUPIM

MI SANU, Knez Mihailova 35, Sala 2

** Utorak, 1.10.2002. u 14:15, Biblioteka MI SANU : **

** Dr Ljiljana Brankovic is a Senior Lecturer in the School of Electrical Engineering and Computer Science, University of Newcastle, Australia Title: On the Graceful Tree Conjecture **

** ABSTRACT: In 1967 Rosa defined a beta-labeling of a finite undirected graph G with n edges to be a one-to-one function f from the set of vertices of G to the set {0,1,2,.,n} such that the induced edge labels are all distinct (by an induced label of an edge between vertices u and v we mean |f(u) - f(v)|). In 1972 Golomb called such labeling a graceful labeling and this became the standard name for it. What is today commonly known as Ringel-Kotzig conjecture (also as Graceful Tree Conjecture - GTC) is a claim that all trees have a graceful labeling. In this talk we give the state of art of advances towards this famous conjecture, fondly called a 'disease' of graph theory. **

** NAPOMENA: dr Ljiljana Brankovic ce odrzati i predavanje pod naslovom "Privacy in Statistical Databases and Data Mining" u cetvrtak 3.10.2002. u 13 casova na Elektrotehnickom fakultetu u Beogradu u sali 61 **

** Ponedeljak, 07.10.2002. u 14h, biblioteka MI SANU : **

** Prof. Dimiter Ivanchev Faculty of Applied Mathematics and Computer Science Technical Unuversity of Sofia and Department of Telecommunications New Bulgarian Unuversity, Sofia DEPENDENCE BETWEEN PLANARITY AND DIRECTIVITY OF NETWORKS **

** Abstract: For a given directed and arc capacited network G it is well known how to find those k arcs the removal of which ninimizes the flow value of the maximum flow. These arcs are called k most vital arcs of G. The problem seems to be NP-complete one. In the special case if G is s-t planar network there are some polinomial algorithms for solving it. The analogous problem for finding k most vital nodes can be reduced to the previous one after certain network transformaton. The question arises: if G is directed, connected and s-t planar network, is the transformed network also planar one or it is not? We give two sufficient and necessary conditions for preserving planarity and directivity of the network using this transformation. **

Sreda, 09.10.2002. u 14:15, Biblioteka MI SANU :

* Teodor Gabriel Crainic, Professor Dpartement management et technologie, Universit du Qubec Montral and Director, Intelligent Transportation Systems Laboratory Centre for Research on Transportation Universit de Montral E-mail: theo@crt.umontreal.ca * Freight Exchanges and Fleet Management

Abstract: Electronic business has a significant impact on transportation and logistics activities. In particular, the emergence of electronic auctions impacts carriers and shippers alike. We examine a number of important issues related to the design and operations of electronic freight exchanges: the type of market operation - periodic, continuous, etc. -, the type of market clearance mechanism - combinatorial or not -, design of market rules, the optimization formulations required to determine the participants allocations and the corresponding prices, the associated solution methods, etc. We also examine the need for and the main characteristics of advisors to participants that is, of models and methods that may help carriers to combine efficiently the market information and their own planning and operations procedures, as well as to conduct negotiation on possibly several diverse markets. We describe one class of advisors for container or full load carriers that is tightly coupled to the carriers planning system. The `planning'' component of the advisor determines what bids are interesting and initial prices. It takes the form of a dynamic and stochastic multi-resource allocation formulation. The "negotiation" component conducts the actual participation to the auctions. Its structure depends on the time allocated to bid.

** RUKOVODIOCI SEMINARA **

** Vera Kovacevic-Vujcic Milan Drazic **