As many readers may know, graph theory is a fundamental branch of mathematics that
explores networks made up of nodes and edges, focusing on their paths, structures, and …

This book introduces important results and techniques in property testing, where the goal is
to design algorithms that decide whether their input satisfies a predetermined property in …

Graph theory, a branch of mathematics, studies relationships between entities using vertices
and edges. In this field, Uncertain Graph Theory has emerged to capture the uncertainties …

We study straight-line drawings of graphs where the vertices are placed in convex position
in the plane, ie, convex drawings. We consider two families of graph classes with nice …

We initiate the study of the testability of properties in arbitrary planar graphs. We prove that
bipartiteness can be tested in constant time. The previous bound for this class of graphs was …

We study the query complexity of graph isomorphism in the property testing model for dense
graphs. We give an algorithm that makes n 1+ o (1) queries, improving on the previous best …

In this paper we provide sub-linear algorithms for several fundamental problems in the
setting in which the input graph excludes a fixed minor, ie, is a minor-free graph. In …

The challenges posed by big data in the 21st Century are complex: Under the previous
common sense, we considered that polynomial-time algorithms are practical; however …

Property testing algorithms are highly efficient algorithms that come with probabilistic
accuracy guarantees. For a property P, the goal is to distinguish inputs that have P from …

We consider the problem of untangling a given (non-planar) straight-line circular drawing δ
G of an outerplanar graph G=(V, E) into a planar straight-line circular drawing of G by shifting …