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Bounds for regular induced subgraphs of strongly regular graphs
Evans, Rhys J.
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.
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