AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete graph for 2k > h. We prove here that there is no k-critically h-connected connected graph with order ⪰h + k − 2 for 2k > h + 1. We prove also that there is no k-critically h-connected line graph for 2k > h. The last result was conjectured by Maurer and Slater. We apply in our proofs a method introduced by Mader
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractThe vertex connectivity of a graph G is denoted by κ(G) and the minimum degree of G is denot...
It is proved that every non-complete, finite digraph of connectivity number k has a fragment F conta...
AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete...
AbstractEntringer and Slater proved that every k-critically h-connected graph with h⩽2k+1 contains a...
AbstractA well-known conjecture of P. J. Slater says that there is no non-complete (k + 1)-criticall...
AbstractChartrand, Kaugars and Lick proved that every critically h-connected graph contains a vertex...
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractWe prove that every n-connected graph G of sufficiently large order contains a connected gra...
AbstractA graph G which is n-connected (but not (n + 1)-connected)is defined to be k-critical if for...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractLet G be a graph with K(G)=h. A vertex v of G is called k-critical if k(G−v)=h−1. Generalizi...
AbstractLet G be a graph with K(G)=h. A vertex v of G is called k-critical if k(G−v)=h−1. Generalizi...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractThe vertex connectivity of a graph G is denoted by κ(G) and the minimum degree of G is denot...
It is proved that every non-complete, finite digraph of connectivity number k has a fragment F conta...
AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete...
AbstractEntringer and Slater proved that every k-critically h-connected graph with h⩽2k+1 contains a...
AbstractA well-known conjecture of P. J. Slater says that there is no non-complete (k + 1)-criticall...
AbstractChartrand, Kaugars and Lick proved that every critically h-connected graph contains a vertex...
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractWe prove that every n-connected graph G of sufficiently large order contains a connected gra...
AbstractA graph G which is n-connected (but not (n + 1)-connected)is defined to be k-critical if for...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractLet G be a graph with K(G)=h. A vertex v of G is called k-critical if k(G−v)=h−1. Generalizi...
AbstractLet G be a graph with K(G)=h. A vertex v of G is called k-critical if k(G−v)=h−1. Generalizi...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractThe vertex connectivity of a graph G is denoted by κ(G) and the minimum degree of G is denot...
It is proved that every non-complete, finite digraph of connectivity number k has a fragment F conta...
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