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

collaborators

Showing 2024Show all

7 papers · 1 filter

cs.DS2024

Fast and Simple $(1 + ε) Δ$ -Edge-Coloring of Dense Graphs

Abhishek Dhawan

Let $ε \in (0, 1)$ and $n, Δ \in N$ be such that $Δ = Ω (max {\frac{l o g n}{ε}, (\frac{1}{ε} lo g \frac{1}{ε})^{2}})$ . Given an $n$ -vertex $m$ -edge…

cs.DS2024★ 1 cited

Palette Sparsification for Graphs with Sparse Neighborhoods

Abhishek Dhawan

A seminal palette sparsification result of Assadi, Chen, and Khanna states that in every $n$ -vertex graph of maximum degree $Δ$ , sampling $Θ (lo g n)$ colors per vertex from $\{1, \…

cs.DS2024

A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time

Abhishek Dhawan

We present a simple $(1 + ε) Δ$ -edge-coloring algorithm for graphs of maximum degree $Δ = Ω (lo g n / ε)$ with running time $O (m lo g^{3} n / ε^{3})$ …

cs.DS2024

A linear-time algorithm for $(1 + ε) Δ$ -edge-coloring

Anton Bernshteyn, Abhishek Dhawan

We present a randomized algorithm that, given a constant $ε > 0$ , outputs a proper $(1 + ε) Δ$ -edge-coloring of an $m$ -edge simple graph $G$ of maximum degree $Δ \geq 1/ ε$ in $O (m)$ tim…

cs.CC2024

The Low-Degree Hardness of Finding Large Independent Sets in Sparse Random Hypergraphs

Abhishek Dhawan, Yuzhou Wang

We study the algorithmic task of finding large independent sets in Erdos-Renyi $r$ -uniform hypergraphs on $n$ vertices having average degree $d$ . Krivelevich and Sudakov showed tha…

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…

Fast and Simple (1+ε)Δ-Edge-Coloring of Dense Graphs

Palette Sparsification for Graphs with Sparse Neighborhoods

A Simple Algorithm for Near-Vizing Edge-Coloring in Near-Linear Time

A linear-time algorithm for (1+ε)Δ-edge-coloring

The Low-Degree Hardness of Finding Large Independent Sets in Sparse Random Hypergraphs

Bounds for the independence and chromatic numbers of locally sparse graphs

Coloring locally sparse graphs

Fast and Simple $(1 + ε) Δ$ -Edge-Coloring of Dense Graphs

A linear-time algorithm for $(1 + ε) Δ$ -edge-coloring