Abstract
A near perfect matching is a matching saturating all but one vertex in a graph. Let G be a connected graph. If any n independent edges in G are contained in a near perfect matching where n is a positive integer and n ⩽ ( | V ( G ) | - 2 ) / 2 , then G is said to be defect n-extendable. If deleting any k vertices in G where k ⩽ | V ( G ) | - 2 , the remaining graph has a perfect matching, then G is a k-critical graph. This paper first shows that the connectivity of defect n-extendable graphs can be any integer. Then the characterizations of defect n-extendable graphs and ( 2 k + 1 ) -critical graphs using M-alternating paths are presented.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
