A matching is extendable in a graph G if G has a perfect matching containing it.A distance q matching is a matching such that the distance between any two distinct matching edges is at least q.In this paper,we prove t...A matching is extendable in a graph G if G has a perfect matching containing it.A distance q matching is a matching such that the distance between any two distinct matching edges is at least q.In this paper,we prove that any distance 2k-3 matching is extendable in a connected and locally(k-1)-connected K1,k-free graph of even order.Furthermore,we also prove that any distance q matching M in an r-connected and locally(k-1)-connected K1,k-free graph of even order is extendable provided that|M|is bounded by a function on r,k and q.Our results improve some results in[J.Graph Theory 93(2020),5–20].展开更多
基金Supported in part by the National Natural Science Foundation of China(11631014)the National Key Research&Development Program of China(2017YFC0908405)。
文摘A matching is extendable in a graph G if G has a perfect matching containing it.A distance q matching is a matching such that the distance between any two distinct matching edges is at least q.In this paper,we prove that any distance 2k-3 matching is extendable in a connected and locally(k-1)-connected K1,k-free graph of even order.Furthermore,we also prove that any distance q matching M in an r-connected and locally(k-1)-connected K1,k-free graph of even order is extendable provided that|M|is bounded by a function on r,k and q.Our results improve some results in[J.Graph Theory 93(2020),5–20].
