Polychromatic colorings of plane graphs

N. Alon, R. Berke, K. Buchin, M. Buchin, P. Csorba, S. Shannigrahi, B. Speckmann, P. Zumstein

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

10 Citations (Scopus)


We show that the vertices of any plane graph in which every face is of size at least g can be colored by (3g Àý 5)=4 colors so that every color appears in every face. This is nearly tight, as there are plane graphs that admit no vertex coloring of this type with more than (3g+1)=4 colors. We further show that the problem of determining whether a plane graph admits a vertex coloring by 3 colors in which all colors appear in every face is NP-complete even for graphs in which all faces are of size 3 or 4 only. If all faces are of size 3 this can be decided in polynomial time.
Original languageEnglish
Title of host publicationProceedings 24th Annual ACM Symposium on Computational Geometry (SoCG'08, College Park MD, USA, June 9-11, 2008)
Place of PublicationNew York NY
PublisherAssociation for Computing Machinery, Inc
ISBN (Print)978-1-60558-071-5
Publication statusPublished - 2008


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