Add to ORKGThe aim of this paper is to prove that if s > 1 and G is a graph of order n > 4s + 6 satisfying 2 > (4n - 4s - 3) / 3 ; then every matching of G lies on a cycle of length at least n-s and hence, in a path of length at least n - s + 1
summary:In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\geq ...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractS. Locke proved that the cycle space of a 3-connected nonhamiltonian graph with minimum degr...
In this paper we prove that if G is a (k + 2)-connected graph on n > 3 vertices satisfying P(n + ...
AbstractUsing the property that being s-edge-Hamiltonian is (n+s)-stable, we characterize all 3-conn...
AbstractFor a graph G, let σ2(G) denote the minimum degree sum of two nonadjacent vertices (when G i...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
AbstractA cycle of C of a graph G is called a Dλ-cycle if every component of G − V(C) has order less...
A cycle of C of a graph G is called a Dλ-cycle if every component of G − V(C) has order less than λ....
AbstractLet G be a hamiltonian graph G of order n and maximum degree Δ, and let C(G) denote the set ...
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all l...
AbstractA graph G of order p ⩾ 3 is called n-hamiltonian, 0 ⩽ n ⩽ p − 3, if the removal of any m ver...
AbstractWe study the set of cycle lengths in a hamiltonian graph G of order n with two fixed and non...
AbstractIn 1956, W.T. Tutte proved that a 4-connected planar graph is hamiltonian. Moreover, in 1997...
summary:In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\geq ...
summary:In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\geq ...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractS. Locke proved that the cycle space of a 3-connected nonhamiltonian graph with minimum degr...
In this paper we prove that if G is a (k + 2)-connected graph on n > 3 vertices satisfying P(n + ...
AbstractUsing the property that being s-edge-Hamiltonian is (n+s)-stable, we characterize all 3-conn...
AbstractFor a graph G, let σ2(G) denote the minimum degree sum of two nonadjacent vertices (when G i...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
AbstractA cycle of C of a graph G is called a Dλ-cycle if every component of G − V(C) has order less...
A cycle of C of a graph G is called a Dλ-cycle if every component of G − V(C) has order less than λ....
AbstractLet G be a hamiltonian graph G of order n and maximum degree Δ, and let C(G) denote the set ...
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all l...
AbstractA graph G of order p ⩾ 3 is called n-hamiltonian, 0 ⩽ n ⩽ p − 3, if the removal of any m ver...
AbstractWe study the set of cycle lengths in a hamiltonian graph G of order n with two fixed and non...
AbstractIn 1956, W.T. Tutte proved that a 4-connected planar graph is hamiltonian. Moreover, in 1997...
summary:In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\geq ...
summary:In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\geq ...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractS. Locke proved that the cycle space of a 3-connected nonhamiltonian graph with minimum degr...