A graph is called Hamiltonian connected if it contains a Hamiltonian path between any two
distinct vertices. In the past, we proved the Hamiltonian path and cycle problems for general …

The longest and Hamiltonian path problems are well-known NP-hard problems in graph
theory. Despite many applications of these problems, they are still open for many classes of …

A Hamiltonian path (cycle) of a graph is a simple path (cycle) in which each vertex of the
graph is visited exactly once. The Hamiltonian path (cycle) problem is to determine whether …

Supergrid graphs are derived by computing stitch paths for computerized embroidery
machines. In the past, we have studied the Hamiltonian-related properties of supergrid …

The Hamiltonian path problem on general graphs is well-known to be NP-complete. In the
past, we have proved it to be also NP-complete for supergrid graphs. A graph is called …

Domination problem is a well-known NP-complete problem for general graphs. In this paper,
we will study its three variants, including restrained, independent restrained, and restrained …

Supergrid graphs contain grid graphs and triangular grid graphs as their subgraphs. The
Hamiltonian cycle and path problems for general supergrid graphs were known to be NP …

The longest (s, t)-path problem on supergrid graphs is known to be NP-complete. However,
the complexity of this problem on supergrid graphs with or without holes is still unknown. In …

Consider a graph G with vertex set V (G) and edge set E (G). A subset D of V (G) is said to be
a dominating set of G if every vertex not in D is adjacent to at least one vertex in D. If, in …

The Hamiltonian path and cycle problems are well-known NP-complete problems. A given
graph is Hamiltonian-connected if there exists a Hamiltonian path between any two vertices …