For a positive integer k, a graph G is k-ordered if for every ordered set of k vertices, there is a
cycle that encounters the vertices of the set in the given order. If the cycle is also a …

A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G
containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition …

A simple graph G is k-ordered (respectively, k-ordered hamiltonian), if for any sequence of k
distinct vertices v1,…, vkof G there exists a cycle (respectively, hamiltonian cycle) in G …

A graph G is k-ordered if for every sequence of k distinct vertices of G, there exists a cycle in
G containing these k vertices in the specified order. It is k-ordered-Hamiltonian if, in addition …

It is known that if G is a connected simple graph, then G3 is Hamiltonian (in fact, Hamilton-
connected). A simple graph is k-ordered Hamiltonian if for any sequence v1, v2,…, vk of k …

A graph G is k-ordered if for any sequence of k distinct vertices v 1, v 2,…, vk of G there
exists a cycle in G containing these k vertices in the specified order. In 1997, Ng and Schultz …

We prove that 3-Coloring remains NP-hard on 4-and 5-regular planar Hamiltonian graphs,
strengthening the results of Dailey [Disc. Math.'80] and Fleischner and Sabidussi [J. Graph …

A graph G is k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G
containing these k vertices in the specified order. It is k-ordered Hamiltonian if, in addition …

The Chvátal-Erdös theorems imply that if G is a graph of order n≥ 3 with κ (G)≥ α (G), then
G is hamiltonian, and if κ (G)> α (G), then G is hamiltonian-connected. We generalize these …

A graph G is called k-ordered if for any sequence of k distinct vertices of G, there exists a
cycle in G through these vertices in the given order. A vertex set S is called cyclable in G if …