Shamil Asgarli

activity

20172026

most citedVan Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields

15 citations · 54 across the 30 of their papers we have counts for

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11 papers · 1 filter

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 $χ_{d} (G; k)$ counts the $k$ -colorings of $G$ in which each vertex has at most $d$ neighbors of its own co…

math.CO2026

An Erdős-Ko-Rado theorem for binary codes

Shamil Asgarli, Chi Hoi Yip

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

math.CO2026

Extremal diameters of 3-coloring graphs of trees

Shamil Asgarli, Sara Krehbiel, Simon MacLean +1

Given a tree $T$ , its 3-coloring graph $C_{3} (T)$ has as vertices the proper 3-colorings of $T$ , with edges joining colorings that differ at exactly one vertex. We call the…

math.CO2025

Bell coloring graphs: realizability and reconstruction

Shamil Asgarli, Sara Krehbiel, Simon MacLean

Given a graph $G$ , the Bell $k$ -coloring graph $B_{k} (G)$ has vertices given by partitions of $V (G)$ into $k$ independent sets (allowing empty parts), with two partitions a…

math.CO2025

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.CO2025

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.CO2024

Chromatic quasisymmetric functions of the path graph

Farid Aliniaeifard, Shamil Asgarli, Maria Esipova +3

We show that the chromatic quasisymmetric function (CQF) of a labeled path graph on $n$ vertices is not symmetric unless the labeling is the natural labeling $1, 2, ..., n$ or its…

math.CO2024

Counting subgraphs of coloring graphs

Shamil Asgarli, Sara Krehbiel, Howard W. Levinson +1

The chromatic polynomial $π_{G} (k)$ of a graph $G$ can be viewed as counting the number of vertices in a family of coloring graphs $C_{k} (G)$ associated with (proper) $k$ -co…

math.CO2022★ 7 cited

The EKR-module property of pseudo-Paley graphs of square order

Shamil Asgarli, Sergey Goryainov, Huiqiu Lin +1

We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdős-Ko-Rado (EKR) module property, in a sense that the char…

math.CO2021

The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes

Shamil Asgarli, Chi Hoi Yip

Blokhuis showed that all maximum cliques in Paley graphs of square order have a subfield structure. Recently, it has been shown that in Peisert-type graphs, all maximum cliques are…

math.CO2021★ 15 cited

Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields

Shamil Asgarli, Chi Hoi Yip

A well-known conjecture due to van Lint and MacWilliams states that if $A$ is a subset of $F_{q^{2}}$ such that $0, 1 \in A$ , $∣ A ∣ = q$ , and $a - b$ is a square for each $a,b \in…