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.
|Title of host publication||Proceedings 24th Annual ACM Symposium on Computational Geometry (SoCG'08, College Park MD, USA, June 9-11, 2008)|
|Place of Publication||New York NY|
|Publisher||Association for Computing Machinery, Inc|
|Publication status||Published - 2008|