AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1)-connected for any X⊆V(G) with |X|⩽k. Mader conjectured that for k⩾3 the graph K2k+2-(1-factor) is the unique (2k, k)-graph. We settle this conjecture for k⩽4
AbstractMader [Arch. Math. 23 (1972), 219–224] determined the minimal number of 1-factors in a 2k-co...
AbstractSuppose that n ⩾ 2t + 2 (t ⩾ 17). Let G be a graph with n vertices such that its complement ...
AbstractA subgraph H of a 3-connected finite graph G is called contractible if H is connected and G−...
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractWe prove that every n-connected graph G of sufficiently large order contains a connected gra...
AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete...
AbstractA well-known conjecture of P. J. Slater says that there is no non-complete (k + 1)-criticall...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractIn this paper, counterexamples are given for Kano's conjecture on connected [2,k]-factors an...
AbstractMcCuaig and Ota conjectured that every sufficiently large 3-connected graph G contains a con...
Let G be a noncomplete k -connected graph such that the graphs obtained from contracting any edge in...
AbstractWe show that any line graph contains a set of three vertices which is not included in a smal...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractThe vertex connectivity of a graph G is denoted by κ(G) and the minimum degree of G is denot...
AbstractMader [Arch. Math. 23 (1972), 219–224] determined the minimal number of 1-factors in a 2k-co...
AbstractSuppose that n ⩾ 2t + 2 (t ⩾ 17). Let G be a graph with n vertices such that its complement ...
AbstractA subgraph H of a 3-connected finite graph G is called contractible if H is connected and G−...
AbstractA noncomplete graph G is called an (n, k)-graph if it is n-connected and G−X is not (n−|X|+1...
AbstractLet W ⊆ V in a graph G = (V, E) such that W ∩ X ≠ Ø for each fragment X of G. Then G is defi...
AbstractWe prove that every n-connected graph G of sufficiently large order contains a connected gra...
AbstractA conjecture of Slater states that Kh + 1 is the unique k-critically h-connected noncomplete...
AbstractA well-known conjecture of P. J. Slater says that there is no non-complete (k + 1)-criticall...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractIn this paper, counterexamples are given for Kano's conjecture on connected [2,k]-factors an...
AbstractMcCuaig and Ota conjectured that every sufficiently large 3-connected graph G contains a con...
Let G be a noncomplete k -connected graph such that the graphs obtained from contracting any edge in...
AbstractWe show that any line graph contains a set of three vertices which is not included in a smal...
AbstractMader conjectured that every non-complete k-critically n-connected graph has (2k + 2) pairwi...
AbstractThe vertex connectivity of a graph G is denoted by κ(G) and the minimum degree of G is denot...
AbstractMader [Arch. Math. 23 (1972), 219–224] determined the minimal number of 1-factors in a 2k-co...
AbstractSuppose that n ⩾ 2t + 2 (t ⩾ 17). Let G be a graph with n vertices such that its complement ...
AbstractA subgraph H of a 3-connected finite graph G is called contractible if H is connected and G−...
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