3-choosability of planar graphs with ({= 4)-cycles far apart

Abstrakt

A graph is k-choosable if it can be colored whenever every vertex has a list of at least k available colors. We prove that if cycles of length at most four in a planar graph G are pairwise far apart, then G is 3-choosable.

This is analogous to the problem of Havel regarding 3-colorability of planar graphs with triangles far apart.

Klíčová slova

• Planar graphs
• List coloring