Bounds for regular induced subgraphs of strongly regular graphs

TL;DR

This paper establishes new bounds on the size of regular induced subgraphs in strongly regular graphs, improving previous bounds for infinitely many cases and providing tighter constraints based on graph parameters.

Contribution

It introduces improved bounds for the order of d-regular induced subgraphs in strongly regular graphs, surpassing earlier bounds by Haemers in infinitely many instances.

Findings

New bounds are at least as good as Haemers' bounds.

Upper bounds are improved for infinitely many strongly regular graphs.

Provides tighter constraints based on graph parameters.

Abstract

Given feasible strongly regular graph parameters $(v,k,\lambda,\mu)$ and a non-negative integer $d$, we determine upper and lower bounds on the order of a $d$-regular induced subgraph of any strongly regular graph with parameters $(v,k,\lambda,\mu)$. Our new bounds are at least as good as the bounds on the order of a $d$-regular induced subgraph of a $k$-regular graph determined by Haemers. Further, we prove that for each non-negative integer $d$, our new upper bound improves on Haemers' upper bound for infinitely many strongly regular graphs.