AbstractA graph G is pancyclic if it contains a k-cycle for k = 3,4,…,|V(G)|. In this paper we show a cycle theorem as follows: If C is a hamiltonian cycle of a graph G of order n, where two non-adjacent vertices x,y at distance 2 on C satisfy d(x)+d(y) ⩾ n, then G is either pancyclic, bipartite, missing only the (n − 1)-cycle, or missing the 3-cycle
AbstractLet G be a hamiltonian bipartite graph of order 2n and let C = (x>1,y1,x2,y2,…,xn,yn,x1) be ...
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is...
AbstractA celebrated theorem of Chvátal and Erdős says that G is Hamiltonian if κ(G)⩾α(G), where κ(G...
AbstractA graph G is pancyclic if it contains a k-cycle for k = 3,4,…,|V(G)|. In this paper we show ...
AbstractWe use a recent cycle structure theorem to prove that three well-known hamiltonian degree co...
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all l...
AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree ...
AbstractA graph G of order n is said to be in the class O(n − 1) if deg(u) + deg(ʋ) ⩾ n − 1 for ever...
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all l...
AbstractIn this paper, we prove the following two theorems: (1) If G is a hamiltonian graph of order...
AbstractWe prove the following theorem. LetGbe a graph of ordernand letW⊆V(G). If |W|⩾3 anddG(x)+dG(...
AbstractWe show that a strongly connected digraph with n vertices and minimum degree ⩾ n is pancycli...
Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n...
AbstractA celebrated theorem of Chvátal and Erdős says that G is Hamiltonian if κ(G)⩾α(G), where κ(G...
AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one o...
AbstractLet G be a hamiltonian bipartite graph of order 2n and let C = (x>1,y1,x2,y2,…,xn,yn,x1) be ...
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is...
AbstractA celebrated theorem of Chvátal and Erdős says that G is Hamiltonian if κ(G)⩾α(G), where κ(G...
AbstractA graph G is pancyclic if it contains a k-cycle for k = 3,4,…,|V(G)|. In this paper we show ...
AbstractWe use a recent cycle structure theorem to prove that three well-known hamiltonian degree co...
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all l...
AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree ...
AbstractA graph G of order n is said to be in the class O(n − 1) if deg(u) + deg(ʋ) ⩾ n − 1 for ever...
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all l...
AbstractIn this paper, we prove the following two theorems: (1) If G is a hamiltonian graph of order...
AbstractWe prove the following theorem. LetGbe a graph of ordernand letW⊆V(G). If |W|⩾3 anddG(x)+dG(...
AbstractWe show that a strongly connected digraph with n vertices and minimum degree ⩾ n is pancycli...
Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n...
AbstractA celebrated theorem of Chvátal and Erdős says that G is Hamiltonian if κ(G)⩾α(G), where κ(G...
AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one o...
AbstractLet G be a hamiltonian bipartite graph of order 2n and let C = (x>1,y1,x2,y2,…,xn,yn,x1) be ...
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is...
AbstractA celebrated theorem of Chvátal and Erdős says that G is Hamiltonian if κ(G)⩾α(G), where κ(G...
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