An Induced Subgraph Paradigm for Strongly Regular Graph Constructions

Abstract

How many disjoint copies of some graph $H$ can appear in an induced subgraph of a strongly regular graph? We give upper and lower bounds that depend on the number of vertices in their boundary. This generalizes a result of Lou-Murin which bounds the independence number of a (hitherto still elusive) strongly regular graph with parameters $(99,14,1,2)$. The equality cases suggest alternative structural approaches for potential constructions of such a graph. We show, using computer searches, that one cannot impose certain additional natural conditions for some of the cases.