Elad Tzalik

activity

20222026

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4 papers · 1 filter

math.CO2023

On the Number of Shortest Paths in Graphs

Itai Benjamini, Elad Tzalik

It is proved that the number of shortest paths between two vertices of distance $t$ in a graph with degrees bounded by $Δ$ is at most $2 \cdot (\frac{Δ}{2})^{t}$ . This improves upon th…

cs.DS2023

Color Fault-Tolerant Spanners

Asaf Petruschka, Shay Sapir, Elad Tzalik

We initiate the study of spanners in arbitrarily vertex- or edge-colored graphs (with no "legality" restrictions), that are resilient to failures of entire color classes. When a co…

math.CO2023

Topological expansion for posets and the homological $k$ -connectivity of random $q$ -complexes

Ran Tessler, Elad Tzalik

We study high dimensional expansion beyond simplicial complexes (posets) and focus on $q$ -complexes which are complexes whose basic building blocks are linear spaces. We show that…

math.CO2023

The number of tiles of $Z^{d}$

Itai Benjamini, Gady Kozma, Elad Tzalik

It is proved that the number of subsets of $[n]^{d}$ that tile $Z^{d}$ is $(3^{\frac{1}{3}})^{n^{d} \pm o (n^{d})}$ .

On the Number of Shortest Paths in Graphs

Color Fault-Tolerant Spanners

Topological expansion for posets and the homological k-connectivity of random q-complexes

The number of tiles of Zd

Topological expansion for posets and the homological $k$ -connectivity of random $q$ -complexes

The number of tiles of $Z^{d}$