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

Abstract Let W ⊆ V in a graph G = ( V , E ) such that W ∩ X ≠ O 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 (2 l + 2) distinct ends and bW ⩾ 2 l + 2. (This result implies that Slater's conjecture is true: there exist no ( k , l )-critical graphs with 2 l > k , except K k + 1 .)