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.
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractA graph G with no isolated vertex is total domination vertex critical if for any vertex v of...
AbstractA graph G is called k-critical if G is k-chromatic but every proper subgraph of G has chroma...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractSumner and Blitch defined a graph G to be k-y-critical if y(G) = k and y(G + uv) = k - 1 for...
AbstractFor k⩾0, ϱk(G) denotes the Lick-White vertex partition number of G. A graph G is called (n, ...
AbstractA graph G which is n-connected (but not (n + 1)-connected)is defined to be k-critical if for...
AbstractA graph G is called k-critical if χ(G) = k and χ(G − e) < χ(G) for each edge e of G, where χ...
AbstractWe prove that Kχ(G) is the only vertex critical graph G with χ(G)⩾Δ(G)⩾6 and ω(H(G))⩽⌊Δ(G)2⌋...
AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete...
A graph G is said to be k- γc-critical if the connected domination number of G, γc(G), is k and γc(G...
AbstractA graph G is said to be k-critical if it has chromatic number k but every proper subgraph of...
AbstractA graph G is said to be n-factor-critical if G−T has a perfect matching for every T⊂V(G) wit...
A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is (k − 1)–colo...
Let G be a graph of order p. Let g(x) and f (x) be two nonnegative integer-valued functions dened on...
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractA graph G with no isolated vertex is total domination vertex critical if for any vertex v of...
AbstractA graph G is called k-critical if G is k-chromatic but every proper subgraph of G has chroma...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractSumner and Blitch defined a graph G to be k-y-critical if y(G) = k and y(G + uv) = k - 1 for...
AbstractFor k⩾0, ϱk(G) denotes the Lick-White vertex partition number of G. A graph G is called (n, ...
AbstractA graph G which is n-connected (but not (n + 1)-connected)is defined to be k-critical if for...
AbstractA graph G is called k-critical if χ(G) = k and χ(G − e) < χ(G) for each edge e of G, where χ...
AbstractWe prove that Kχ(G) is the only vertex critical graph G with χ(G)⩾Δ(G)⩾6 and ω(H(G))⩽⌊Δ(G)2⌋...
AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete...
A graph G is said to be k- γc-critical if the connected domination number of G, γc(G), is k and γc(G...
AbstractA graph G is said to be k-critical if it has chromatic number k but every proper subgraph of...
AbstractA graph G is said to be n-factor-critical if G−T has a perfect matching for every T⊂V(G) wit...
A graph G is k-critical if it has chromatic number k, but every proper subgraph of G is (k − 1)–colo...
Let G be a graph of order p. Let g(x) and f (x) be two nonnegative integer-valued functions dened on...
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractA graph G with no isolated vertex is total domination vertex critical if for any vertex v of...
AbstractA graph G is called k-critical if G is k-chromatic but every proper subgraph of G has chroma...
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