We look at a variant of the Hamilton circuit problem, where the input is restricted to hexagonal grid graphs. A hexagonal grid graph has a vertex set that is a subset of the grid points of a regular hexagonal tiling of the plane and edges corresponding to hexagon sides. We show that Hamilton circuit in hexagonal grid graphs is NP-complete.
A grid graph is a node-induced finite subgraph of the infinite grid. It is rectangular if its set of nodes is the product of two intervals. Given a rectangular grid graph and two of its nodes, we give necessary and sufficient conditions for the graph to have a Hamilton path betwe
In this paper we study connectivity and hamiltonicity properties of the topological grid graphs, which are a natural type of planar graphs associated with finite subgraphs of the usual square lattice graph of the plane. The main results are as follows. The shortness coefficient o
The purpose of this paper is to develop an algorithm to determine the Hamilton Circuit in a given graph of degree three. This algorithm will find Hamilton Circuit in polynomial steps. We got some properties; these properties are combined to develop the above mentioned algorithm.
In the paper [Fendley et al., J. Phys. A: Math. Gen., 38 (2005), pp. 315-322], Fendley, Schoutens and van Eerten studied the hard square model at negative activity. They found analytical and numerical evidence that the eigenvalues of the transfer matrix with periodic boundary wer
An edge irregular total k-labeling of a graph G = (V,E) is a labeling φ : V ∪ E → {1, 2, . . . , k} such that the total edge-weights wt(xy) = φ(x) + φ(xy) + φ(y) are different for all pairs of distinct edges. The minimum k for which the graph G has an edge irregular total k-label