Adva Mond

collaborators

8 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

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

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

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…