Abhishek Dhawan

activity

20232026

most citedPalette Sparsification for Graphs with Sparse Neighborhoods

1 citations · 3 across the 19 of their papers we have counts for

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14 papers · 1 filter

math.CO2026

Random independent sets in uncrowded hypergraphs

Abhishek Dhawan, Lina Li, Abhishek Methuku +2

Given any fixed integer $k \geq 2$ and sufficiently large $d$ , we show that the largest possible fractional chromatic number of a $k$ -uniform $d$ -degenerate uncrowded hypergraph $H$ …

math.CO2026

Fractional DP-colorings of $d$ -degenerate locally sparse graphs

Abhishek Dhawan, Huy Nguyen, Rohan A. Rathi

Bernshteyn, Kostochka, and Zhu (2020) introduced the notion of fractional DP-coloring, which generalizes both fractional coloring and fractional list coloring. Among several founda…

math.CO2026

Sharp bounds for the fractional chromatic number of high-girth $d$ -degenerate graphs

Peter Allen, Abhishek Dhawan, Jonathan A. Noel

Martinsson and Steiner recently proved that the fractional chromatic number of any $d$ -degenerate triangle-free graph $G$ satisfies $χ_{f} (G) = O (\frac{d}{l o g d})$ . They…

math.CO2026

List coloring uncrowded hypergraphs at the shattering threshold

Abhishek Dhawan, Abhishek Methuku, Minh-Quan Vo

Improving an earlier bound of Frieze and Mubayi, Iliopoulos showed that any $k$ -uniform uncrowded hypergraph of maximum degree $Δ$ has list chromatic number at most $(1+o(1))(k-1)\…

math.CO2026

The strong chromatic index of $K_{t, t}$ -free graphs

Richard Bi, Peter Bradshaw, Abhishek Dhawan +1

A strong edge coloring of a graph $G$ is an edge coloring $ϕ : E (G) \to N$ such that each color class forms an induced matching in $G$ . The strong chromatic index…

math.CO2026

Fractional coloring via entropy

Abhishek Dhawan

In recent work, Martinsson and Steiner proved that triangle-free $d$ -degenerate graphs have fractional chromatic number $χ_{f} (G) = O (\frac{d}{l o g d})$ . Here, we introduc…

math.CO2025

Choosability of multipartite hypergraphs

Peter Bradshaw, Abhishek Dhawan, Nhi Dinh +2

A $k$ -uniform hypergraph (or $k$ -graph) $H = (V, E)$ is $k$ -partite if $V$ can be partitioned into $k$ sets $V_{1}, \dots, V_{k}$ such that each edge in $E$ contains precisely one ver…

math.CO2025

Independent sets and colorings of $K_{t, t, t}$ -free graphs

Abhishek Dhawan, Oliver Janzer, Abhishek Methuku

Alon, Krivelevich, and Sudakov conjectured in 1999 that every $F$ -free graph of maximum degree at most $Δ$ has chromatic number $O (Δ/ lo g Δ)$ . This was previously known only for a…

math.CO2025

Toward Vu's conjecture

Peter Bradshaw, Abhishek Dhawan, Abhishek Methuku +1

In 2002, Vu conjectured that graphs of maximum degree $Δ$ and maximum codegree at most $ζ Δ$ have chromatic number at most $(ζ + o (1)) Δ$ . Despite its importance, the conjecture has re…

math.CO2025

Balanced colorings of Erdős-Rényi hypergraphs

Abhishek Dhawan, Yuzhou Wang

An $r$ -uniform hypergraph $H = (V, E)$ is $r$ -partite if there exists a partition of the vertex set into $r$ parts such that each edge contains exactly one vertex from each part. W…

math.CO2024

Bounds for the independence and chromatic numbers of locally sparse graphs

Abhishek Dhawan

In this note we consider a more general version of local sparsity introduced recently by Anderson, Kuchukova, and the author. In particular, we say a graph $G = (V, E)$ is $(k, r)$ …

math.CO2024★ 1 cited

Coloring locally sparse graphs

James Anderson, Abhishek Dhawan, Aiya Kuchukova

A graph $G$ is $k$ -locally sparse if for each vertex $v \in V (G)$ , the subgraph induced by its neighborhood contains at most $k$ edges. Alon, Krivelevich, and Sudakov showed that f…

math.CO2023★ 1 cited

List colorings of $k$ -partite $k$ -graphs

Abhishek Dhawan

A $k$ -uniform hypergraph (or $k$ -graph) $H = (V, E)$ is $k$ -partite if $V$ can be partitioned into $k$ sets $V_{1}, \dots, V_{k}$ such that each edge in $E$ contains precisely one ver…

math.CO2023

Balanced independent sets and colorings of hypergraphs

Abhishek Dhawan

A $k$ -uniform hypergraph $H = (V, E)$ is $k$ -partite if $V$ can be partitioned into $k$ sets $V_{1}, \dots, V_{k}$ such that every edge in $E$ contains precisely one vertex from each…

Random independent sets in uncrowded hypergraphs

Fractional DP-colorings of d-degenerate locally sparse graphs

Sharp bounds for the fractional chromatic number of high-girth d-degenerate graphs

List coloring uncrowded hypergraphs at the shattering threshold

The strong chromatic index of Kt,t​-free graphs

Fractional coloring via entropy

Choosability of multipartite hypergraphs

Independent sets and colorings of Kt,t,t​-free graphs

Toward Vu's conjecture

Balanced colorings of Erdős-Rényi hypergraphs

Bounds for the independence and chromatic numbers of locally sparse graphs

Coloring locally sparse graphs

List colorings of k-partite k-graphs

Balanced independent sets and colorings of hypergraphs

Fractional DP-colorings of $d$ -degenerate locally sparse graphs

Sharp bounds for the fractional chromatic number of high-girth $d$ -degenerate graphs

The strong chromatic index of $K_{t, t}$ -free graphs

Independent sets and colorings of $K_{t, t, t}$ -free graphs

List colorings of $k$ -partite $k$ -graphs