Quadrangulations and 4-color-critical graphs

Carsten Thomassen
2004 Journal of combinatorial theory. Series B (Print)  
Erd + os asked if the removal of few edges in a large 4-color-critical graph always leaves a 3-chromatic graph. Erd + os and Hajnal asked if a graph is 3-colorable if all its induced subgraphs can be made bipartite by the omission of few edges (relative to the number of vertices). We answer both problems, which are stated in Bollobas' monograph Extremal Graph Theory from 1978, in the negative. r
doi:10.1016/j.jctb.2003.11.003 fatcat:rz2cuhkbjnhujcpqnsg4odvmp4