In 2007, Arkin et al. [3] initiated a systematic study of the complexity of the Hamiltonian cycle problem on square, triangular, or hexagonal grid graphs, restricted to polygonal, thin, superthin, degree-bounded, or solid grid graphs. They solved many combinations of these problems, proving them either polynomially solvable or NP-complete, but left three combinations open. In this paper, we pro...

For an integer n > 2, the triangular graph has vertex set the 2-subsets of {1, . . . , n} and edge set the pairs of 2-subsets intersecting at one point. Such graphs are known to be halved graphs of bipartite rectagraphs, which are connected triangle-free graphs in which every 2-path lies in a unique quadrangle. We refine this result and provide a characterisation of connected locally triangular...

Determining the maximum outerplanar subgraph of a given graph is known to be an NP-complete problem. In the literature there are no earlier experiment on approximating the maximum outerplanar subgraph problem. In this paper we compare solution quality and running times of different heuristics for finding maximum outerplanar subgraphs. We compare a greedy heuristic against a triangular cactus he...

The matching preclusion number of a graph is the minimum number of neither edges whose deletion in a graph has a neither perfect matching nor an almost perfect matching. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently the conditional matching preclusion number of a graph was introduced to look for sets beyond those induced by a single...

This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and t...

An injective function f : V (G)→ {0, 1, 2, . . . , q} is an odd sum labeling if the induced edge labeling f∗ defined by f∗(uv) = f(u) + f(v), for all uv ∈ E(G), is bijective and f∗(E(G)) = {1, 3, 5, . . . , 2q − 1}. A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper, we have studied the odd sum property of the subdivision of the triangular snake, quadrilatera...

We present a method for hierarchical image segmentation and feature extraction. This method builds upon the combination of the detection of image spectral discontinuities using Canny edge detection and the image Laplacian, followed by the construction of a hierarchy of segmented images of successively reduced levels of details. These images are represented as sets of polygonized pixel patches (...

A stable cutset in a graph is a stable set whose deletion disconnects the graph. It was conjectured by Caro and proved by Chen and Yu that any graph with n vertices and at most 2n − 4 edges contains a stable cutset. The bound is tight, as we will show that all graphs with n vertices and 2n− 3 edges without stable cutset arise recursively glueing together triangles and triangular prisms along an...

The paper describes a parallel-pipeline implementation of solving grid equations using the modified alternating-triangular iterative method (MATM), obtained by numerically mathematical physics. greatest computational costs at this are on stages system linear algebraic (SLAE) with lower triangular and upper non-triangular matrices. An algorithm for SLAE matrix graphics accelerator NVIDIA CUDA te...

We investigate the well-known problem of counting graph imbeddings on all oriented surfaces with a focus on graphs that are obtained by pasting together two root-edges of another base graph. We require that the partitioned genus distribution of the base graph with respect to these root-edges be known and that both root-edges have two 2-valent endpoints. We derive general formulas for calculatin...