Abstract
A conjecture by A. Hoffmann-Ostenhof suggests that any connected cubic graph G contains a spanning tree T for which every component of G−E(T) is a K1, a K2, or a cycle. We show that any cubic graph G contains a spanning forest F for which every component of G−E(F) is a K2 or a cycle, and that any connected graph G≠K1 with maximal degree at most 3 contains a spanning forest F without isolated vertices for which every component of G−E(F) is a K1, a K2 or a cycle. We also prove a related statement about path-factorizations of graphs with maximal degree 3.
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.
