Random Structures & Algorithms

We analyse the size of an independent set in a random graph on n vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily, and, for each vertex in turn, place it in the independent set unless it ...

Given a graph on n vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length n visiting each vertex once and with pairwise different colours on the edges. Similarly for even n a rainbow perfect matching is a ...

We study the problem of reconstructing a low-rank matrix, where the input is an n×m matrix M over a field F and the goal is to reconstruct a near-optimal matrix M' that is low-rank and close to M under some distance function Δ. Furthermore, the ...

Let H be a fixed graph and G a subcritical graph class. In this paper we show that the number of occurrences of H as a subgraph in a graph in G of order n, chosen uniformly at random, follows a normal limiting distribution with linear expectation and ...

The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of a sequence of ...

For each n∈ï ź, let Qn be a uniform rooted quadrangulation, endowed with an appropriate measure, of size n conditioned to have rn vertices in its root block. We prove that for a suitable function rn, after rescaling graph distance by 2140·rn1/4,Qn ...