The extendability of matchings in strongly regular graphs

Abstract

A graph G of even order v is called t-extendable if it contains a perfect matching, t k/2, where λ is the number of common neighbors of any two adjacent vertices and μ is the number of common neighbors of any two non-adjacent vertices. Our results are close to being best possible as there are strongly regular graphs of valency k that are not ⌈k/2⌉-extendable. We show that the extendability of many strongly regular graphs of valency k is at least ⌈k/2⌉-1 and we conjecture that this is true for all primitive strongly regular graphs. We obtain similar results for strongly regular graphs of odd order.