Abstract
Suppose that G is a planar graph with maximum degree Δ and without intersecting 4-cycles, that is, no two cycles of length 4 have a common vertex. Let χ ″ ( G ) , χ l ′ ( G ) and χ l ″ ( G ) denote the total chromatic number, list edge chromatic number and list total chromatic number of G , respectively. In this paper, it is proved that χ ″ ( G ) = Δ + 1 if Δ ≥ 7 , and χ l ′ ( G ) = Δ and χ l ″ ( G ) = Δ + 1 if Δ ( G ) ≥ 8 . Furthermore, if G is a graph embedded in a surface of nonnegative characteristic, then our results also hold.
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.
