Abstract
Abstract This paper provides tight lower bounds on the maximum genus of a regular graph in terms of its cycle rank. The main tool is a relatively simple theorem that relates lower bounds with the existence (or non-existence) of induced subgraphs with odd cycle rank that are separated from the rest of the graph by cuts of size at most three. Lower bounds on the maximum genus are obtained by bounding from below the size of these odd subgraphs. As a special case, upper-embeddability of a class of graphs is caused by an absence of such subgraphs. A well-known theorem stating that every 4-edge-connected graph is upper-embeddable is a straightforward corollary of the employed method.
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.
