The independence number of a tree decomposition is the maximum of the independence
numbers of the subgraphs induced by its bags. The tree-independence number of a graph is …

One of the most celebrated results in Parameterized Complexity is the Bidimensionality
theory of Demaine et al.[J. ACM, 2005], which has yielded, over the past two decades …

We develop simple and general techniques to obtain faster (near-linear time) static
approximation algorithms, as well as efficient dynamic data structures, for four fundamental …

An outerstring graph is the intersection graph of curves lying inside a disk with one endpoint
on the boundary of the disk. We show that an outerstring graph with $ n $ vertices has …

We study exact algorithms for Euclidean TSP in R d. In the early 1990s algorithms with n O
(√ n) running time were presented for the planar case, and some years later an algorithm …

We initiate a systematic study of approximation schemes for fundamental optimization
problems on disk graphs, a common generalization of both planar graphs and unit-disk …

Let F be a set of n objects in the plane and let G×(F) be its intersection graph. A balanced
clique-based separator of G×(F) is a set S consisting of cliques whose removal partitions …

In a disk graph, every vertex corresponds to a disk in $\mathbb {R}^ 2$ and two vertices are
connected by an edge whenever the two corresponding disks intersect. Disk graphs form an …

We revisit the classic task of finding the shortest tour of n, points in d-dimensional Euclidean
space, for any fixed constant d\geqslant2. We determine the optimal dependence on ε in the …

Research in graph theory remains essential for driving progress in both scientific and
technological fields. Within this area, studies on graph algorithms and those leveraging …