On the existence of (k.l)-critical graphs

AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defined to be W-locally (k, l)-critical if κ(G − W′) = k − W′ holds for every W′ ⊆ W with. In this note we give a short proof for the following recent result of Su: every non-complete W-locally (k, l)-critical graph has (2l + 2) distinct ends and bW⩾ 2l + 2. (This result implies that Slater's conjecture is true: there exist no (k, l)-critical graphs with 2l > k, except Kk + 1.