Minimum Sum Edge Colorings of Multicycles

In the minimum sum edge coloring problem, we aim to assign natural numbers to edges of a graph, so that adjacent edges receive different numbers, and the sum of the numbers assigned to the edges is minimum. The {\em chromatic edge strength} of a graph is the minimum number of colors required in a minimum sum edge coloring of this graph. We study the case of multicycles, defined as cycles with parallel edges, and give a closed-form expression for the chromatic edge strength of a multicycle, thereby extending a theorem due to Berge. It is shown that the minimum sum can be achieved with a number of colors equal to the chromatic index. We also propose simple algorithms for finding a minimum sum edge coloring of a multicycle. Finally, these results are generalized to a large family of minimum cost coloring problems

Az új algoritmusok és kódolási eljárások alkalmazása a mobil hírközlésben és informatikában = Application of new algorithms and coding procedures in mobile communications and computing

A kutatási munka során az alábbi résztémákban értünk el eredményeket: - mobil IP, - all IP hálózatok, - útkeresési algoritmusok, - hívásátadási algoritmusok, - mobil technológiák együttműködése, - a szolgáltatás minősége (QoS), - a mobil és informatikai hálózatok és rendszerek biztonsági kérdései, - több-felhasználós vétel, - kódosztásos többszörös hozzáférés, - forgalmi modellezés, - kódkonstrukció kódosztásos technológiákhoz, - kvantum számítástechnikai eljárások, - gráfelmélet, - kombinatorikus optimalizálás. A fenti szakterületeken végzett kutatásaink eredményei közül azokat emeljük ki, amelyeket az alábbi témákban értünk el: - A heterogén mobil hálózatok együttműködési problémái, - A mobil Internet Protokoll alkalmazásával kapcsolatos vizsgálatok, - Többfelhasználós detekciós módszerek a kódosztásos többszörös hozzáféréses mobil rendszerekben, - A heterogén mobil hálózatok forgalmi modellezése, - A mobil informatikai és távközlési hálózatok, rendszerek és szolgáltatások - biztonsági kérdései, - Kvantum számítástechnika és mérnöki alkalmazásai, - Útkeresési és csatornakijelölési algoritmusok fejlesztése és vizsgálata mobil hálózatok számára, alkalmazott gráfelmélet. A kutatásban résztvevők az eredményeket három megvédett PhD disszertációban, egy benyújtás előtt álló akadémiai doktori értekezésben és több beadás előtt álló PhD értekezésben használták fel. A tudományos iskola publikációs listája 135 elemből áll. | The members of the Scientific School have got new results in the following scientific fields: - Mobile IP, all IP networks, - Routing algorithms, - Hand-over algorithms, - Interworking of heterogeneous mobile technologies, - Quality of services (QoS), - Security problems of mobile and information networks and systems, - Multi-user detection, - Code division multiple access, - Traffic modeling, - Code construction for code division technologies, - Quantum computing, - Graph theory, - Combinatorial optimization. On the above mentioned scientific field we have the most important results in the following areas: - Interoperability issues of heterogeneous mobile networks, - Investigations on the applicability of mobile Internet Protocol, - Multi-user detection methods in code division multiple access systems, - Traffic models of heterogeneous mobile networks, - Security issues of mobile information and telecommunication networks, systems and services, - Quantum computing and its engineering applications, - Development and research of routing and channel assigning algorithms for mobile networks, application of the graph theory. The participants of the research used their results in three defended PhD theses, in a dissertation for DSc title, and in some other PhD theses before the final process. The number of the publications of the Scientific School is 135

Combinatorics

Combinatorics is a fundamental mathematical discipline that focuses on the study of discrete objects and their properties. The present workshop featured research in such diverse areas as Extremal, Probabilistic and Algebraic Combinatorics, Graph Theory, Discrete Geometry, Combinatorial Optimization, Theory of Computation and Statistical Mechanics. It provided current accounts of exciting developments and challenges in these fields and a stimulating venue for a variety of fruitful interactions. This is a report on the meeting, containing extended abstracts of the presentations and a summary of the problem session

A study of the total coloring of graphs.

The area of total coloring is a more recent and less studied area than vertex and edge coloring, but recently, some attention has been given to the Total Coloring Conjecture, which states that each graph\u27s total chromatic number xT is no greater than its maximum degree plus two. In this dissertation, it is proved that the conjecture is satisfied by those planar graphs in which no vertex of degree 5 or 6 1ies on more than three 3-cycles. The total independence number aT is found for some families of graphs, and a relationship between that parameter and the size of a graph\u27s minimum maximal matching is discussed. For colorings with natural numbers, the total chromatic sum ST is introduced, as is total strength (oT of a graph. Tools are developed for proving that a total coloring has minimum sum, and this sum is found for some graphs including paths, cycles, complete graphs, complete bipartite graphs, full binary trees, and some hypercubes. A family of graphs is found for which no optimal total coloring maximizes the smallest color class. Lastly, the relationship between a graph\u27s total chromatic number and its total strength is explored, and some graphs are found that require more than their total chromatic number of colors to obtain a minimum sum

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Efficient enumeration of graph orientations with sources

International audienceAn orientation of an undirected graph is obtained by assigning a direction to each of its edges. It is called cyclic when a directed cycle appears, and acyclic otherwise. We study efficient algorithms for enumerating the orientations of an undirected graph. To get the full picture, we consider both the cases of acyclic and cyclic orientations, under some rules specifying which nodes are the sources (i.e. their incident edges are all directed outwards). Our enumeration algorithms use linear space and provide new bounds for the delay, which is the maximum elapsed time between the output of any two consecutively listed solutions. We obtain a delay of O(m) for acyclic orientations and ˜Oand˜ and˜O(m) for cyclic ones. When just a single source is specified, these delays become O(m · n) and O(m · h + h 3), respectively, where h is the girth of the graph without the given source. When multiple sources are specified, the delays are the same as in the single source case.

Renormalization: an advanced overview

We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.Comment: Review, 130 pages, 33 figures; v2: misprints corrected, refs. added, minor improvements; v3: some changes to sect. 5, refs. adde