We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...
Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...
This paper examines the binning of two types of parts with random characteristics, so that a componentwise monotonic evaluation criterion exhibits a minimum deviation to a given target value over all possible realizations. The optimal matching classes are ...
This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between n nodes, with patterns that may change over time, the objective is to servi ...
Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...
We study in this thesis the asymptotic behavior of optimal paths on a random graph model, the configuration model, for which we assign continuous random positive weights on its edges.
We start by describing the asymptotic behavior of the diameter and the f ...
Let c denote the largest constant such that every C-6-free graph G contains a bipartite and C-4-free subgraph having a fraction c of edges of G. Gyori, Kensell and Tompkins showed that 3/8
Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...
We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in e ...
