摘要
Suppose that G is a planar cubic graph withχi(G)>5.We show that ifχi(H)<χi(G)for each planar cubic graph H of order less thanG,thenG is either a 3-connected simple planar cubic graph,or a planar graph obtained from a simple cubic 3-connected planar graph by adding some earrings.This shows that a minimum non-5-injectively colorable simple planar cubic graph must be 3-connected.
基金
This research was supported by the National Natural Science Foundation of China(Nos.11571180 and 11331003)
the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.17KJB110010).
