For every integer r≥3r\ge 3r≥3 and every finite graph FFF satisfying χ(F)=r\chi(F)=rχ(F)=r and tw(F)≥r\operatorname{tw}(F)\ge rtw(F)≥r, there exist constants cF>0c_F>0cF>0 and n0(F)n_0(F)n0(F) such that, for every intege…