Fine registration of point clouds plays an important role in data analysis in Terrestrial Laser Scanning (TLS). This work proposes a block-to-point fine registration approach to correct the errors of point clouds from TLS and of geodetic networks observed using total stations. Based on a reference coordinate system, the block-to-point estimation is performed to obtain representative points. The...

We propose a discrete weighted Helmholtz decomposition for edge element functions. The decomposition is orthogonal in a weighted L inner product and stable uniformly with respect to the jumps in the discontinuous weight function. As an application, the new Helmholtz decomposition is applied to demonstrate the quasi-optimality of a preconditioned edge element system for solving a saddle-point Ma...

The Tree Decomposition Conjecture by Barát and Thomassen states that for every tree T there exists a natural number k(T ) such that the following holds: If G is a k(T )-edge-connected simple graph with size divisible by the size of T , then G can be edge-decomposed into subgraphs isomorphic to T . So far this conjecture has only been verified for paths, stars, and a family of bistars. We prove ...

Let G be a connected graph on n vertices, and let ; ; and be edge-disjoint cycles in G such that (i) ; (resp. ;) are vertex-disjoint and (ii) jj + jj = jj+ jj = n, where jj denotes the length of. We say that ; ; and yield two edge-disjoint hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e; f; g and h such that each of (? feg) S (? ffg) S fg; hg and (? fgg) S (...

For a connected graph G = (V,E), a set W ⊆ V is called a Steiner set of G if every vertex of G is contained in a Steiner W -tree of G. The Steiner number s(G) of G is the minimum cardinality of its Steiner sets and any Steiner set of cardinality s(G) is a minimum Steiner set of G. For a minimum Steiner set W of G, a subset T ⊆ W is called a forcing subset for W if W is the unique minimum Steine...

A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. Our main result implies that, given any optimal colouring a sufficiently large complete K2n, there exists decomposition K2n into isomorphic spanning trees. This settles conjectures Brualdi–Hollingsworth (from 1996) and Constantine 2002) for graphs.

A set S ⊆ V (G) is called a geodetic if every vertex of G lies on shortest u-v path for some u, v ∈ S, the minimum cardinality among all sets number and denoted by . C chromatic contains vertices different colors in G, geo-chromatic Sc both set. The G. In this paper, we determine 2-cartesian product standard graphs like complete graphs, cycles paths.

In the geodetic convexity, a set of vertices S graph G is convex if all belonging to any shortest path between two lie in . The hull H ( ) smallest containing If = V ), then cardinality h minimum number complementary prism GḠ arises from disjoint union and Ḡ by adding edges perfect matching corresponding A autoconnected both are connected. Motivated previous work, we study for prisms graphs. Wh...

A set S of vertices of a graph G is a geodetic set if every vertex of G lies in an interval between two vertices from S. The size of a minimum geodetic set in G is the geodetic number g(G) of G. We find that the geodetic number of the lexicographic product G ∘H for non-complete graphs H lies between 2 and 3g(G). We characterize the graphs G and H for which g(G ∘H) = 2, as well as the lexicograp...