DOI: 10.1002/jgt.70110 ISSN: 0364-9024
A Note on Extendable Sets of Colorings and Rooted Minors
Zdeněk Dvořák, Jan M. SwartABSTRACT
DeVos and Seymour proved that for every set of 3‐colorings of a set of vertices, there exists a plane graph with vertices of incident with the outer face such that a 3‐coloring of extends to a 3‐coloring of if and only if it belongs to . We prove a generalization of this claim for ‐colorings of ‐rooted‐‐minor‐free ‐minor‐free graphs.