Abstract
Lebesgue (1940) proved that every normal plane map of girth 5 has a path on three vertices (3-path) of degree 3. A description is tight if no its parameter can be strengthened, and no alternative dropped. Borodin et al. (2013) gave a tight description of 3-paths in arbitrary normal plane maps.We give seven tight descriptions of 3-paths in triangle-free normal plane maps. Furthermore, we prove that this set of descriptions is complete, which is a result of a bit new type in the structural theory of plane graphs.
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.
