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The sandglass conjecture beyond cancellative pairs
Adva Mond, Victor Souza, Leo Versteegen
The sandglass conjecture, posed by Simonyi, states that if a pair of families of subsets of is recovering then . We improve the best known upper bo…
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 -vertex-connected graph and every vertex in , there are spanning trees of such that, for every v…
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…
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…
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 . We show that a typical co…