Shamil Asgarli

activity

20242026

collaborators

14 papers

math.CO2026

Coloring graphs as complete graph invariants

Shamil Asgarli, Sara Krehbiel, Howard W. Levinson

We investigate the extent to which the $k$ -coloring graph $C_{k} (G)$ uniquely determines the base graph $G$ and the number of colors $k$ . The vertices of $\mathcal{C}_{k}…

math.CO2026

Defective chromatic polynomials

Shamil Asgarli, Tamsen Whitehead McGinley, Nicholas Xue

For a graph $G$ and an integer $d \geq 0$ , the defective chromatic polynomial $I ¨ _{d} (G; k)$ counts the $k$ -colorings of $G$ in which each vertex has at most $d$ neighbors of its own c…

math.CO2026

Improved lower bounds for the maximum order of an induced acyclic subgraph

Shamil Asgarli, Donald Falkenhagen, Kaya Hoshi

Computing the cardinality of a maximum induced acyclic vertex set in a digraph is NP-hard. Since finding an exact solution is computationally difficult, a fruitful approach is to e…

math.CO2026

An ErdÅs-Ko-Rado theorem for binary codes

Shamil Asgarli, Chi Hoi Yip

We study intersecting families of words from the ErdÅs-Ko-Rado perspective. When the alphabet size is $2$ , a maximum intersecting family is not necessarily a star. However, we pro…

math.AG2026

Hypersurfaces passing through the Galois orbit of a point

Shamil Asgarli, Jonathan Love, Chi Hoi Yip

Asgarli, Ghioca, and Reichstein proved that if $K$ is a field with $∣ K ∣ > 2$ , then for any positive integers $d$ and $n$ , and separable field extension $L / K$ with degree $m=\binom{n+…

math.NT2026

Collision of orbits for families of polynomials defined over fields of positive characteristic

Shamil Asgarli, Dragos Ghioca

Let $L$ be a field of positive characteristic $p$ with a fixed algebraic closure $L$ , and let $I^\pm_{1}, I^\pm_{2}, I^^{2} \in L$ . For an integer $d \geq 2$ , we consider the family of pol…

Coloring graphs as complete graph invariants

Defective chromatic polynomials

Improved lower bounds for the maximum order of an induced acyclic subgraph

An ErdÅs-Ko-Rado theorem for binary codes

Hypersurfaces passing through the Galois orbit of a point

Collision of orbits for families of polynomials defined over fields of positive characteristic

An ErdÅs-Ko-Rado theorem for binary codes