Abstract
Let G be a maximal plane graph of diameter at most two. Let χl(G) and χd(G) denote the list chromatic number and the diagonal chromatic number of G, respectively. In this paper, we study the structure of G and show the following results: (1) χl(G) ≤ 4; and (2) χd(G) ≤ 9, and χd(G)=9 if and only if G is a specific graph on nine vertices.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.