1 citations · 3 across the 12 of their papers we have counts for
14 papers · 1 filter
Perfect matchings and Hamilton cycles in uniform attachment graphs
Huseyin Acan
We study Hamilton cycles and perfect matchings in a uniform attachment graph. In this random graph, vertices are added sequentially, and when a vertex is created, it makes …
Giant descendant trees, matchings and independent sets in the age-biased attachment graphs
Huseyin Acan, Alan Frieze, Boris Pittel
We study two models of an age-biased graph process: the -version of the preferential attachment graph model (PAM) and the uniform attachment graph model (UAM), with attachme…
On connectivity, conductance and bootstrap percolation for a random k-out, age-biased graph
Hüseyin Acan, Boris Pittel
A uniform attachment graph (with parameter ), denoted in the paper, is a random graph on the vertex set , where each vertex makes selections from …
Counting unlabeled interval graphs
Hüseyin Acan
We improve the bounds on the number of interval graphs on vertices. In particular, denoting by the quantity in question, we show that as $n\to \in…
Permutations With Equal Orders
Huseyin Acan, Charles Burnette, Sean Eberhard +2
Let be the probability that two independent, uniformly random permutations of have the same order, and let be the probability that they are in the same conjugac…
Disproof of a packing conjecture of Alon and Spencer
Huseyin Acan, Jeff Kahn
A 1992 conjecture of Alon and Spencer says, roughly, that the ordinary random graph typically admits a covering of a constant fraction of its edges by edge-disjoint, ne…
Proof of an entropy conjecture of Leighton and Moitra
Hüseyin Acan, Pat Devlin, Jeff Kahn
We prove the following conjecture of Leighton and Moitra. Let be a tournament on and the set of permutations of . For an arc of , let $A_{uv}=\{σ\in S_…
Forests of chord diagrams with a given number of trees
Huseyin Acan
In this short note, we find the number of forests of chord diagrams with a given number of trees and a given number of chords.
On a uniformly random chord diagram and its intersection graph
Huseyin Acan
A chord diagram refers to a set of chords with distinct endpoints on a circle. The intersection graph of a chord diagram is defined by substituting the chords of …
On the covariances of outdegrees in random plane recursive trees
Hüseyin Acan, Paweł Hitczenko
In 2005 Janson, extending earlier work of Mahmoud, Smythe, and Szymański, established the joint asymptotic normality of the outdegrees of a random plane recursive tree. In particul…
On a memory game and preferential attachment graphs
Huseyin Acan, Pawel Hitczenko
In a recent paper Velleman and Warrington analyzed the expected values of some of the parameters in a memory game, namely, the length of the game, the waiting time for the first ma…
On random trees obtained from permutation graphs
Huseyin Acan, Pawel Hitczenko
A permutation gives rise to a graph ; the vertices of are the letters in the permutation and the edges of …
Formation of a giant component in the intersection graph of a random chord diagram
Huseyin Acan, Boris Pittel
We study the number of chords and the number of crossings in the largest component of a random chord diagram when the chords are sparsely crossing. This is equivalent to studying t…
On the connected components of a random permutation graph with a given number of edges
Huseyin Acan, Boris Pittel
A permutation of [n] induces a graph on [n] such that the edges of the graph correspond to inversion pairs of the permutation. This graph is connected if and only if the correspond…