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Tucker's lemma states that if we triangulate the unit disc centered at the origin and color the vertices with {1, 1,2, 2} in an antipodal way (if vertical bar z vertical bar = 1, then the sum of the colors of z and -z is zero), then there must be an edge F ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2009
This paper's focus is the following family of problems, denoted k-ECSS, where k denotes a positive integer: given a graph (V, E) and costs for each edge, find a minimum-cost subset F of E such that (V, F) is k-edge-connected. For k=1 it is the spanning tre ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010
An optimal linear-time algorithm for interprocedural register allocation in high level synthesis is presented. Historically, register allocation has been modeled as a graph coloring problem, which is nondeterministic polynomial time-complete in general; ho ...
We study two decomposition problems in combinatorial geometry. The first part of the thesis deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-decomposable if there is a constant m such that any m-fold coveri ...
We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends pe ...
Starting from the basic problem of reconstructing a 2-dimensional image given by its projections on two axes, one associates a model of edge coloring in a complete bipartite graph. The complexity of the case with k=3 colors is open. Variations and special ...
Extensions and variations of the basic problem of graph coloring are introduced. The problem consists essentially in finding in a graph G a k-coloring, i.e., a partition V-1,...,V-k of the vertex set of G such that, for some specified neighborhood (N) over ...
We study the problem where a robot has to pick up items of different sizes which are stored along a corridor. A natural requirement is that the items have to be collected in decreasing order of their sizes. We deal with various systems according to the loc ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...
A string graph is the intersection graph of a collection of continuous arcs in the plane. We show that any string graph with in edges can be separated into two parts of roughly equal size by the removal of O(m(3/4)root log m) vertices. This result is then ...
