AbstractWe show that for all positive ε, an integer N(ε) exists such that if G is any graph of order n⩾N(ε) with minimum degree δ⩾32√n then G contains a cycle of length 2l for each integer l, 2⩽l⩽δ⧸(16 + ε)
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree ...
AbstractIn this paper we solve a conjecture of P. Erdös by showing that if a graph Gn has n vertices...
Our main result is the following theorem. Let k ≥ 2 be an integer, G be a graph of sufficiently larg...
AbstractWe study the set of cycle lengths in a hamiltonian graph G of order n with two fixed and non...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractBondy and Vince proved that every graph with minimum degree at least three contains two cycl...
AbstractBondy and Vince proved that every graph with minimum degree at least three contains two cycl...
A classic result of Dirac states that if G is a 2-connected graph of order n with minimum degree δ ≥...
AbstractWe show that for each ℓ⩾4 every sufficiently large oriented graph G with δ+(G),δ−(G)⩾⌊|G|/3⌋...
AbstractLet G be a 2-connected bipartite graph with bipartition (A, B), where |A| ≥ |B|. It is shown...
AbstractThis paper determines lower bounds on the number of different cycle lengths in a graph of gi...
AbstractBondy conjectured a common generalization of various results in hamiltonian graph theory con...
AbstractWe prove that every Hamiltonian graph with n vertices and m edges has cycles with more than ...
AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one o...
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree ...
AbstractIn this paper we solve a conjecture of P. Erdös by showing that if a graph Gn has n vertices...
Our main result is the following theorem. Let k ≥ 2 be an integer, G be a graph of sufficiently larg...
AbstractWe study the set of cycle lengths in a hamiltonian graph G of order n with two fixed and non...
AbstractN. Alon [J. Graph Theory 10 (1986), 123–127] proved that if the minimum degree of a graph G ...
AbstractBondy and Vince proved that every graph with minimum degree at least three contains two cycl...
AbstractBondy and Vince proved that every graph with minimum degree at least three contains two cycl...
A classic result of Dirac states that if G is a 2-connected graph of order n with minimum degree δ ≥...
AbstractWe show that for each ℓ⩾4 every sufficiently large oriented graph G with δ+(G),δ−(G)⩾⌊|G|/3⌋...
AbstractLet G be a 2-connected bipartite graph with bipartition (A, B), where |A| ≥ |B|. It is shown...
AbstractThis paper determines lower bounds on the number of different cycle lengths in a graph of gi...
AbstractBondy conjectured a common generalization of various results in hamiltonian graph theory con...
AbstractWe prove that every Hamiltonian graph with n vertices and m edges has cycles with more than ...
AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one o...
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree ...
AbstractIn this paper we solve a conjecture of P. Erdös by showing that if a graph Gn has n vertices...
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