Max-cut and extendability of matchings in distance-regular graphs

A connected graph G of even order v is called t-extendable if it contains a perfect matching, t < v/2 and any matching of t edges is contained in some perfect matching. The extendability of G is the maximum t such that G is t-extendable. Since its introduction by Plummer in the 1980s, this combinatorial parameter has been studied for many classes of interesting graphs. In 2005, Brouwer and Haemers proved that every distance-regular graph of even order is 1-extendable and in 2014, Cioabă and Li showed that any connected strongly regular graph of even order is 3-extendable except for a small number of exceptions. Research supported in part by NSA grant H98230-13-1-0267 and NSF grant DMS-1600768. Research partially supported by the 100 talents program of Chinese Academy of Sciences. Research is also partially supported by the National Natural Science Foundation of China (No. 11471009). Research supported by the University Dissertation Fellows award by University of Delaware.