Abstract
We prove a structural theorem of Lebesgue's type concerning the existence of certain types of vertices in 3-connected plane graphs. This theorem is then applied to the proof such that the cyclic chromatic number χ c (G)⩽k+2 for k= max{40,Δ ∗(G)} , where Δ ∗(G) denotes the size of the largest face of G. This confirms a conjecture by Plummer and Toft for Δ ∗(G)⩾40 .
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.
