Lyuben Lichev

activity

20202026

most citedOn the modularity of 3-regular random graphs and random graphs with given degree sequences

4 citations · 21 across the 45 of their papers we have counts for

collaborators

Showing 2025Show all

10 papers · 1 filter

math.CO2025

Sharp thresholds, hitting times and the power of choice for random geometric graphs

Dawid Ignasiak, Lyuben Lichev

We consider a random geometric graph process where random points $(X_{i})_{i \geq 1}$ are embedded consecutively in the $d$ -dimensional unit torus $T^{d}$ , and every two points…

math.PR2025

Diameter and mixing time of the giant component in the percolated hypercube

Michael Anastos, Sahar Diskin, Lyuben Lichev +1

We consider bond percolation on the $d$ -dimensional binary hypercube with $p = c / d$ for fixed $c > 1$ . We prove that the typical diameter of the giant component $L_{1}$ is of order $Θ(d)…

math.CO2025

Approximate Itai-Zehavi conjecture for random graphs

Lawrence Hollom, Lyuben Lichev, Adva Mond +2

A famous conjecture by Itai and Zehavi states that, for every $d$ -vertex-connected graph $G$ and every vertex $r$ in $G$ , there are $d$ spanning trees of $G$ such that, for every v…

math.CO2025

Cycle lengths in the percolated hypercube

Michael Anastos, Sahar Diskin, Joshua Erde +3

Let $Q_{p}^{d}$ be the random subgraph of the $d$ -dimensional binary hypercube obtained after edge-percolation with probability $p$ . It was shown recently by the authors that, for ever…

math.CO2025

Monotonicity and decompositions of random regular graphs

Lawrence Hollom, Lyuben Lichev, Adva Mond +2

In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameter…

math.CO2025

Spanning trees of bounded degree in random geometric graphs

Michael Anastos, Sahar Diskin, Dawid Ignasiak +2

We determine the sharp threshold for the containment of all $n$ -vertex trees of bounded degree in random geometric graphs with $n$ vertices. This provides a geometric counterpart o…

math.CO2025

Nearly spanning cycle in the percolated hypercube

Michael Anastos, Sahar Diskin, Joshua Erde +3

Let $Q^{d}$ be the $d$ -dimensional binary hypercube. We form a random subgraph $Q_{p}^{d} \subseteq Q^{d}$ by retaining each edge of $Q^{d}$ independently with probability $p$ . We show that,…

math.CO2025

Universality of the matching number in percolated regular graphs

Sahar Diskin, Mihyun Kang, Lyuben Lichev

Fix a sequence of $d$ -regular graphs $(G_{d})_{d \in N}$ and denote by $G_{d, p}$ the graph obtained from $G_{d}$ after edge-percolation with probability $p = c / d$ , for a constant…

math.CO2025

Colouring random Hasse diagrams and box-Delaunay graphs

Zhihan Jin, Matthew Kwan, Lyuben Lichev

Fix $d \geq 2$ and consider a uniformly random set $P$ of $n$ points in $[0, 1]^{d}$ . Let $G$ be the Hasse diagram of $P$ (with respect to the coordinatewise partial order), or alterna…

math.CO2025

Explosive appearance of cores and bootstrap percolation on lattices

Ivailo Hartarsky, Lyuben Lichev

Consider the process where the $n$ vertices of a square $2$ -dimensional torus appear consecutively in a random order. We show that typically the size of the $3$ -core of the corresp…