Abstract
A plane graph is dual-eulerian if it has an eulerian tour with the property that the same sequence of edges also forms an eulerian tour in the dual graph. Dual-eulerian graphs are of interest in the design of CMOS VLSI circuits. Every dual-eulerian plane graph also has an eulerian Petrie (left–right) tour thus we consider series-parallel extensions of plane graphs to graphs, which have eulerian Petrie tours. We reduce several special cases of extensions to the problem of finding hamiltonian cycles. In particular, a 2-connected plane graph G has a single series parallel extension to a graph with an eulerian Petrie tour if and only if its medial graph has a hamiltonian cycle.
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.
