works on
approximation algorithms 1combinatorial bounds 1envy-freeness 1fair division 1randomized algorithms 1

From the 1 of 8 linked papers with an AI index.

collaborators

8 papers

math.CO2026

Graph Eigenvalues and Projection Constants

Varun Sivashankar, Quanyu Tang, Tanay Wakhare

For an integer , let denote the th largest adjacency eigenvalue of a graph . For every graph on vertices and every , we prove \[ λ_…

cs.GT2026

A Linear Bound on the Rainbow Cycle Number and Approximate EFX

Varun Sivashankar

The paper proves that the rainbow cycle number grows linearly with the dimension, which yields a partial (1‑ε)-EFX allocation for any fair‑division instance with only O(√(n/ε)) una…

math.CO2026

Pseudoshattering Pairs

Noga Alon, Varun Sivashankar

For two vectors , consider the bipartite graph with two copies of in which on the left is joined to on the right if for some coordinat…

math.CO2026

An Improved Lower Bound for the Erdős-Lovász Cover Number Problem

Varun Sivashankar

Let be the minimum number of edges in an -uniform intersecting hypergraph with cover number . Erdős and Lovász proved the lower bound . We first give…

math.CO2026

Tree-independence number and forbidden induced subgraphs: excluding a -vertex path and a -biclique

Maria Chudnovsky, Julien Codsi, J. Pascal Gollin +2

We show that for every positive integer there exists an integer such that every graph that contains no induced subgraph isomorphic to either the -vertex path or…

math.CO2026

Upper bound on the -th eigenvalue of a graph

Varun Sivashankar

We prove a general upper bound on the -th adjacency eigenvalue of a graph. For , we show that \[ λ_k(G)\le \frac{(k-2)\sqrt{k+1}+2}{2k(k-1)}\,n-1 \] for every graph …