Matchings and Nonrainbow Colorings

Zdeněk Dvořák, Stanislav Jendrol', Daniel Král', Gyula Pap
2009 SIAM Journal on Discrete Mathematics  
We show that the maximum number of colors that can be used in a vertex coloring of a cubic 3-connected plane graph G that avoids a face with vertices of mutually distinct colors (a rainbow face) is equal to n 2 + µ * − 2, where n is the number of vertices of G and µ * is the size of the maximum matching of the dual graph G * .
doi:10.1137/060675927 fatcat:oijob43zdfgvja5h23cg7anu2i