5 research outputs found
Hamiltonian paths in the square of a tree
Abstract. We introduce a new family of graphs for which the Hamiltonian path problem is non-trivial and yet has a linear time solution. The square of a graph G = (V, E), denoted as G 2 , is a graph with the set of vertices V , in which two vertices are connected by an edge if there exists a path of length at most 2 connecting them in G