We consider the following firefighter problem on a graph G = (V, E). Initially, a fire breaks out at a vertex v of G. In each subsequent time unit, a firefighter protects one vertex, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefighter is to save as many vertices as possible. Let sn(v) denote the maximum number of vertices the firefigh...

A total weighting of a graph G is a mapping f which assigns to each element z ∈ V (G)∪E(G) a real number f(z) as its weight. The vertex sum of v with respect to f is φf (v) = ∑ e∈E(v) f(e) + f(v). A total weighting is proper if φf (u) 6= φf (v) for any edge uv of G. A (k, k′)-list assignment is a mapping L which assigns to each vertex v a set L(v) of k permissible weights, and assigns to each e...

We study the Minimum Spanning Caterpillar Problem (MSCP) in a graph where each edge has two costs, spine (path) cost and leaf cost, depending on whether it is used as a spine or a leaf edge. The goal is to find a spanning caterpillar in which the sum of its edge costs is the minimum. We show that the problem has a linear time algorithm when a tree decomposition of the graph is given as part of ...

The quadratic travelling salesman problem (QTSP) is to find a least cost Hamiltonian cycle in an edge-weighted graph. We define a restricted version of QTSP, the kneighbour TSP (TSP(k)), and give a linear time algorithm to solve TSP(k) on a Halin graph for k ≤ 3. This algorithm can be extended to solve TSP (k) on any fully reducible class of graphs for any fixed k in polynomial time. This resul...

Beirat • Comité consultatif Prof. Dr. Boi Faltings (EPFL Lausanne), Prof. Dr. Stefan Klein (Universität Koblenz-Landau), Dr. Ernst Lebsanft (Synlogic AG, Binningen), Prof. Dr. Rudolf Marty (IFA Informatik, Zürich), Prof. Dr. Moira C. Norrie (ETH Zürich), Prof. Dr. Hans-Jörg Schek (ETH Zürich), Dr. Hans Stienen (Synscape, Binningen), Helmut Thoma (ITpro AG Basel), Dr. Reinhold Thurner (Herrliber...

3 Stefan Thiele, Bernhard M. Fuchs, Nagappa Ramaiah, Rudolf Amann 4 5 6 1 Max Planck Institute for Marine Microbiology, Celsiusstrasse 1, D-28359 Bremen, 7 Germany 8 2 National Institute of Oceanography, Dona Paula, Goa 403004, India 9 10 Section: Microbial Ecology 11 12 # corresponding author 13 contact: Max Planck Institute for Marine Microbiology, Celsiusstrasse 1, D-28359 14 Bremen, Germany...

A Lombardi drawing of a graph is a drawing where edges are represented by circular arcs that meet at each vertex v with perfect angular resolution 360◦/deg(v) [3]. It is known that Lombardi drawings do not always exist, and in particular, that planar Lombardi drawings of planar graphs do not always exist [1], even when the embedding is not fixed. Existence of planar Lombardi drawings is known f...

A set S of n points is 2-color universal for a graph G on n vertices if for every proper 2-coloring of G and for every 2-coloring of S with Research was supported by the project 1M0545 of the Ministry of Education of the Czech Republic and by the grant SVV-2010-261313 (Discrete Methods and Algorithms). Viola Mészáros was also partially supported by OTKA grant K76099 and by European project IST-...

This paper describes tight extended formulations for independent set. The first formulation is for arbitrary independence systems and has size O(n+ μ), where μ denotes the number of inclusion-wise maximal independent sets. Consequently, the extension complexity of the independent set polytope of graphs is O(1.4423). The size O(2n) of the second extended formulation depends on the treewidth tw o...

Suçun nitelikli şekline teşebbüsün mümkün olup olmadığı sorunu ceza hukukçuları tarafından uzun zamandır tartışılmaktadır. Bu tartışma hiç şüphesiz özellikle kanunilik ilkesi ve fiilin ağırlığıyla orantılı bir belirlenebilmesi açısından önem taşımaktadır. çalışmada söz konusu mesele, suç yolunun geldiği aşama itibarıyla halin gerçekleştiği durumlar ile suça etki eden nedenin planına dahil olduğ...