Samenvatting
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.
Originele taal-2 | Engels |
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Titel | Proceedings 24th Annual ACM Symposium on Computational Geometry (SoCG'08, College Park MD, USA, June 9-11, 2008) |
Plaats van productie | New York NY |
Uitgeverij | Association for Computing Machinery, Inc |
Pagina's | 338-345 |
ISBN van geprinte versie | 978-1-60558-071-5 |
DOI's | |
Status | Gepubliceerd - 2008 |