Add to ORKGA graph is \emph{hamiltonian-connected} if every pair of vertices can be connected by a hamiltonian path, and it is \emph{hamiltonian} if it contains a hamiltonian cycle. Every hamiltonian-connected graph is hamiltonian, however we also construct families of nonhamiltonian graphs with `many' hamiltonian paths, where 'many' is interpreted with respect to the number of pairs of vertices connected by hamiltonian paths. We then consider minimal graphs that are hamiltonian-connected; we show that any order-$n$ graph that is hamiltonian-connected graphs must have $\geq 3n/2$ edges, and we construct an infinite family of graphs realizing this minimum.Comment: v2: 12 pages, 6 figures. Substantial re-write including new results and removing result...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
AbstractIn 2005, Rahman and Kaykobad introduced the Rahman-Kaykobad condition for the research of Ha...
Clark proved that L(G) is hamiltonian if G is a connected graph of order n 2 6 such that deg u + deg...
A graph is hamiltonian-connected if every pair of vertices can be connected by a hamiltonian path, a...
A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph is Hamilt...
In 1857, the Irish mathematician Sir William Hamilton(1805-1865) invented a game of travelling aroun...
AbstractIn 2005, Rahman and Kaykobad introduced the Rahman-Kaykobad condition for the research of Ha...
In this paper we prove that if G is a (k + 2)-connected graph on n > 3 vertices satisfying P(n + ...
AbstractSince finding whether a graph has a Hamiltonian path or Hamiltonian cycle are both NP-comple...
AbstractA graph G of order p ⩾ 3 is called n-hamiltonian, 0 ⩽ n ⩽ p − 3, if the removal of any m ver...
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is...
AbstractIn this paper, an alternative closure operation to the one introduced in [2] is given. For a...
AbstractA geometric graph is a graph embedded in the plane in such a way that vertices correspond to...
A Hamiltonian path is a spanning path in a graph i.e. a path through every vertex. In this paper we ...
A graph G is Hamiltonian-connected if every two vertices of G are connected by a Hamilton path. A bi...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
AbstractIn 2005, Rahman and Kaykobad introduced the Rahman-Kaykobad condition for the research of Ha...
Clark proved that L(G) is hamiltonian if G is a connected graph of order n 2 6 such that deg u + deg...
A graph is hamiltonian-connected if every pair of vertices can be connected by a hamiltonian path, a...
A graph G is Hamiltonian if it has a spanning cycle. The problem of determining if a graph is Hamilt...
In 1857, the Irish mathematician Sir William Hamilton(1805-1865) invented a game of travelling aroun...
AbstractIn 2005, Rahman and Kaykobad introduced the Rahman-Kaykobad condition for the research of Ha...
In this paper we prove that if G is a (k + 2)-connected graph on n > 3 vertices satisfying P(n + ...
AbstractSince finding whether a graph has a Hamiltonian path or Hamiltonian cycle are both NP-comple...
AbstractA graph G of order p ⩾ 3 is called n-hamiltonian, 0 ⩽ n ⩽ p − 3, if the removal of any m ver...
An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is...
AbstractIn this paper, an alternative closure operation to the one introduced in [2] is given. For a...
AbstractA geometric graph is a graph embedded in the plane in such a way that vertices correspond to...
A Hamiltonian path is a spanning path in a graph i.e. a path through every vertex. In this paper we ...
A graph G is Hamiltonian-connected if every two vertices of G are connected by a Hamilton path. A bi...
AbstractA new sufficient condition for a graph to be Hamiltonian is given that does not require that...
AbstractIn 2005, Rahman and Kaykobad introduced the Rahman-Kaykobad condition for the research of Ha...
Clark proved that L(G) is hamiltonian if G is a connected graph of order n 2 6 such that deg u + deg...