In this paper, various properties of particular type of Hamiltonian graph and it's edge-disjoint Hamiltonian circuits have been discussed. It has been found that the intersection graph obtained from Euler Diagram is not Hamiltonian. The graph H(3m + 7, 6m + 14) for m ? 1, which is planner, regular of degree four, non-bipartite but Hamiltonian graph , has perfect matching 4 with nonrepeated...

Let V be a set of curves in the plane. The corresponding intersection graph has V as the set of vertices, and two vertices are connected by an edge if and only if the two corresponding curves intersect in the plane. It is shown that the set of intersection graphs of curves in the plane is a proper subset of the set of all undirected graphs. Furthermore, the set of intersection graphs of straigh...

The carrier profile for InAs films grown on GaP is modeled as a first-order approximation which assumes that 90° edge dislocation intersections and the threading dislocation intersections act as shallow donors. Due to dislocation annihilation during growth, the threading dislocation intersection density decreases as the inverse of the distance x from the InAs/GaP interface, D(x)5D0x0 /(x0 1x), ...

We derive several algorithms for curves and surfaces represented using normal coordinates. The normal coordinate representation is a very succinct representation of curves and surfaces. For embedded curves, for example, its size is logarithmically smaller than a representation by edge intersections in a triangulation. Consequently, fast algorithms for normal representations can be exponentially...

We first present new structural properties of a two-pair in various graphs. A twopair is used in a well-known characterization of weakly chordal graphs. Based on these properties, we prove the main theorem: a graph G is a weakly chordal (K2,3, 4P2, P2 ∪ P4, P6,H1,H2,H3)-free graph if and only if G is an edge intersection graph of subtrees on a tree with maximum degree 4. This characterizes the ...

We study the simplification of triangular and tetrahedral meshes using techniques based on successive edge collapses, as well as the exploitation of the generated multiple levels of detail for the effective processing of the models. Regarding triangular meshes, we present a method for the construction of progressive hulls, by suitable edge collapses; we use the generated hulls for the accelerat...

Nonconvex polyhedral models of workpieces or robot parts can be directly tested for interference without resorting to a previous decomposition into convex entities Here we show that this in terference detection based on the elemental edge face intersection test can be performed e ciently a strategy based on applicability constraints re duces drastically the set of edge face pairings that have t...

We answer some of the questions raised by Golumbic, Lipshteyn and Stern regarding edge intersection graphs of paths on a grid (EPG graphs). We prove that for any d ≥ 4, in order to represent all n vertex graphs with maximum degree d as edge intersection graphs of n paths, a grid of area Θ(n2) is needed. A bend is a turn of a path at a grid point. Let Bk be the class of graphs that have an EPG r...

In this paper, we introduce a modified fence fill algorithm for filling a polygon. Fence fill algorithm is a modified edge fill algorithm. As opposed to the edge fill algorithm that fills pixels starting from the polygon edge to the maximum screen coordinates, the fence fill algorithm fills pixels bounded by the polygon edge and the fence. This involves large number of calculations to find the ...

An EPG-representation of a graph G is a collection of paths in a plane square grid, each corresponding to a single vertex of G, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In this paper we focus on graphs admitting EPG-representations by paths with at most 2 bends. We show hardness of the recognition problem for this class of graphs, ...