Adva Mond

activity

20182025

most citedMinimum degree edge-disjoint Hamilton cycles in random directed graphs

1 citations · 1 across the 13 of their papers we have counts for

collaborators

18 papers

math.CO2025

The sandglass conjecture beyond cancellative pairs

Adva Mond, Victor Souza, Leo Versteegen

The sandglass conjecture, posed by Simonyi, states that if a pair $(A, B)$ of families of subsets of $[n]$ is recovering then $∣ A ∣∣ B ∣ \leq 2^{n}$ . We improve the best known upper bo…

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

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

On problems in extremal multigraph theory

Victor Falgas-Ravry, Adva Mond, Rik Sarkar +1

A multigraph G is said to be an (s,q)-graph if every s-set of vertices in G supports at most q edges (counting multiplicities). In this paper we consider the maximal sum and produc…

math.CO2025★ 1 cited

Minimum degree edge-disjoint Hamilton cycles in random directed graphs

Asaf Ferber, Adva Mond

In this paper we consider the problem of finding ``as many edge-disjoint Hamilton cycles as possible'' in the binomial random digraph $D_{n, p}$ . We show that a typical $D_{n, p}$ co…

math.CO2024

A note on high-dimensional discrepancy of subtrees

Lawrence Hollom, Lyuben Lichev, Adva Mond +1

For a tree $T$ and a function $f : E (T) \to S^{d}$ , the imbalance of a subtree $T^{'} \subseteq T$ is given by $∣ \sum_{e \in E (T^{'})} f (e) ∣$ . The $d$ -dimensional discrepancy o…

math.CO2024

Discrepancies of spanning trees in dense graphs

Lawrence Hollom, Lyuben Lichev, Adva Mond +1

We address several related problems on combinatorial discrepancy of trees in a setting introduced by Erdős, Füredi, Loebl and Sós. Given a fixed tree $T$ on $n$ vertices and an edg…

math.CO2024

Almost colour-balanced spanning forests in complete graphs

Lawrence Hollom, Adva Mond, Julien Portier

Given $K_{n}$ whose edges are coloured red and blue, and a forest $F$ of order $n$ , we seek embeddings of $F$ with small imbalance, that is, difference between the numbers of red and…

math.PR2024

The Maker-Breaker percolation game on a random board

Vojtěch Dvořák, Adva Mond, Victor Souza

The $(m, b)$ Maker-Breaker percolation game on $(Z^{2})_{p}$ , introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{…

math.CO2024

The asymptotic of off-diagonal online Ramsey numbers for paths

Adva Mond, Julien Portier

We prove that for every $k \geq 10$ , the online Ramsey number for paths $P_{k}$ and $P_{n}$ satisfies $r ~ (P_{k}, P_{n}) \geq \frac{5}{3} n + \frac{k}{9} - 4$ , matching up to a linear te…

cs.CC2023

The complexity of decomposing a graph into a matching and a bounded linear forest

Agnijo Banerjee, João Pedro Marciano, Adva Mond +2

Deciding whether a graph can be edge-decomposed into a matching and a $k$ -bounded linear forest was recently shown by Campbell, H{ö}rsch and Moore to be NP-complete for every $k \g…

math.NT2022

Ternary Egyptian fractions with prime denominator

Adva Mond, Julien Portier

For a prime number $p$ , let $A_{3} (p) = ∣ {m \in N : \exists m_{1}, m_{2}, m_{3} \in N, \frac{m}{p} = \frac{1}{m _{1}} + \frac{1}{m _{2}} + \frac{1}{m _{3}}} ∣$ . In 2019 Luca and Pappal…

math.CO2021

Counting Hamiltonian Cycles in Dirac Hypergraphs

Asaf Ferber, Liam Hardiman, Adva Mond

For $0 \leq ℓ < k$ , a Hamiltonian $ℓ$ -cycle in a $k$ -uniform hypergraph $H$ is a cyclic ordering of the vertices of $H$ in which the edges are segments of length $k$ and every…

math.CO2021

The Maker-Breaker percolation game on the square lattice

Vojtěch Dvořák, Adva Mond, Victor Souza

We study the $(m, b)$ Maker-Breaker percolation game on $Z^{2}$ , introduced by Day and Falgas-Ravry. As our first result, we show that Breaker has a winning strategy for the…

math.CO2019

Turán-type problems for long cycles in random and pseudo-random graphs

Michael Krivelevich, Gal Kronenberg, Adva Mond

We study the Turán number of long cycles in random graphs and in pseudo-random graphs. Denote by $e x (G (n, p), H)$ the random variable counting the number of edges in a largest subgra…

math.CO2019

On the Odd Cycle Game and Connected Rules

Jan Corsten, Adva Mond, Alexey Pokrovskiy +2

We study the positional game where two players, Maker and Breaker, alternately select respectively $1$ and $b$ previously unclaimed edges of $K_{n}$ . Maker wins if she succeeds in cl…

math.CO2019

$H$ -games played on vertex sets of random graphs

Gal Kronenberg, Adva Mond, Alon Naor

We introduce a new type of positional games, played on a vertex set of a graph. Given a graph $G$ , two players claim vertices of $G$ , where the outcome of the game is determined by…

math.CO2018

The Minrank of Random Graphs over Arbitrary Fields

Noga Alon, Igor Balla, Lior Gishboliner +2

The minrank of a graph $G$ on the set of vertices $[n]$ over a field $F$ is the minimum possible rank of a matrix $M \in F^{n \times n}$ with nonzero diagonal entrie…

The sandglass conjecture beyond cancellative pairs

Approximate Itai-Zehavi conjecture for random graphs

Monotonicity and decompositions of random regular graphs

On problems in extremal multigraph theory

Minimum degree edge-disjoint Hamilton cycles in random directed graphs

A note on high-dimensional discrepancy of subtrees

Discrepancies of spanning trees in dense graphs

Almost colour-balanced spanning forests in complete graphs

The Maker-Breaker percolation game on a random board

The asymptotic of off-diagonal online Ramsey numbers for paths

The complexity of decomposing a graph into a matching and a bounded linear forest

Ternary Egyptian fractions with prime denominator

Counting Hamiltonian Cycles in Dirac Hypergraphs

The Maker-Breaker percolation game on the square lattice

Turán-type problems for long cycles in random and pseudo-random graphs

On the Odd Cycle Game and Connected Rules

H-games played on vertex sets of random graphs

The Minrank of Random Graphs over Arbitrary Fields

$H$ -games played on vertex sets of random graphs