Abstract
A graph G is divisible by t if its edge set can be partitioned into t subsets, such that the subgraphs (called factors) induced by the subsets are all isomorphic. It is proved that an r-regular graph G with an even number of vertices v( G) is divisible by r, in such a way that the components of each factor are paths of length 1 and 2, under any of the following conditions: 1. (a) r⩾9 is odd and v(G)> 32(r+1) (r−7) ; 2. (b) r⩾18 and v(G)> 24(r+1) (r−17) ; 3. (c) r=25 or 27, or r⩾29.
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.
