Abstract
In this paper, we prove that for any 3-connected finite graph of order n$$(n\ge 6)$$, the number of contractible non-edges is at most $$\frac{n(n-5)}{2}$$. All the extremal graphs with at least seven vertices are characterized to be 4-connected 4-regular. By generalizing a result of Kriesell (J Comb Theory Ser B 74:192–201, 1998), we also characterize all 3-connected graphs (finite or infinite) that does not contain any contractible non-edges. In particular, every non-complete 3-connected infinite graph contains a contractible non-edge.
Sign-in/Register to access full text options 
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.
