A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. Also, M is said to be a distance d matching if the shortest distance between a pair of edges in M is at least d. A graph G is distance d matchable if every distance d matching is extendable in G, regardless of its size. In this paper, we study the class of distance d matchable graphs. In particular, we prove that for every integer K with k ≥ 3, there exists a positive integer d such that every connected, locally (k − 1)-connected K1,k-free graph of even order is distance d matchable. We also prove that every connected, locally K-connected K1,f-free graph of even order is distance 3 matchable. Furthermore, we make more detailed analysis of K1,4-free graphs and study their distance matching extension properties.
- distance restricted matching extension
- local connectivity
ASJC Scopus subject areas
- Geometry and Topology