Mohamed Omar

activity

20102026

most citedSparse Neural Codes and Convexity

10 citations · 27 across the 20 of their papers we have counts for

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Showing 2026Show all

4 papers · 1 filter

math.CO2026

Multiple Distance Ramsey Bounds For Graphs in Euclidean Spaces

Ayşegül Kula, Mohamed Omar, Jonah Stockwell +1

For a finite set $A \subset R_{> 0}$ and a finite graph $H$ , let $χ_{H} (R^{n}; A)$ be the minimum number of colors required to color $R^{n}$ while avoiding a mon…

math.CO2026

Real Reliability Roots of Simple Graphs are Dense

Mohamed Omar

We prove that the closure of the real roots of all-terminal reliability polynomials is exactly $[- 1, 0] \cup {1}$ , resolving a conjecture of Brown and McMullin and refining the co…

math.CO2026

On a Quadratic Relation Between Stanley-Wilf Limits and Füredi-Hajnal Limits

Mohamed Omar

For a permutation matrix $P$ , let $s_{P}$ denote its Stanley-Wilf limit, the exponential growth rate of the number of $n \times n$ permutation matrices avoiding $P$ . Let $c_{P}$ denote…

math.CO2026

New Perspectives On The Unimodality Of Domination Polynomials

Mohamed Omar

The domination polynomial of a graph $G$ is given by $D (G, x) = \sum_{k = 0}^{n} d_{k} (G) x^{k}$ where $d_{k} (G)$ records the number of $k$ -element dominating sets in $G$ . A conjecture of Alik…