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Note on robust critical graphs with large odd girth
Nstase, E.,Rodl, V.,Siggers, M. North-Holland Pub. Co ; Elsevier Science Ltd 2010 Discrete mathematics Vol.310 No.3
A graph G is (k+1)-critical if it is not k-colourable but G-e is k-colourable for any edge e@?E(G). In this paper we show that for any integers k>=3 and l>=5 there exists a constant c=c(k,l)>0, such that for all n@?, there exists a (k+1)-critical graph G on n vertices with n>n@? and odd girth at least @?, which can be made (k-1)-colourable only by the omission of at least cn<SUP>2</SUP> edges.