Abstract The objective of clustering is to discover natural groups in datasets and identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics data. problem can be seen as detecting inherent separations between a given point set metric space governed by similarity function. pairwise similarities all data objects form weighted graph whose...

Generating terrain models from contour input is still an important process. Most methods have been unsatisfactory, as they either do not preserve the form of minor ridges and valleys, or else they are poor at modelling slopes. A method is described here, based on curve extraction and generalization techniques, that is guaranteed to preserve the topological relationships between curve segments. ...

A face irregular entire k-labeling φ : V ∪E ∪F → {1,2, . . . ,k} of a 2-connected plane graph G = (V,E,F) is a labeling of vertices, edges and faces of G in such a way that for any two different faces f and g their weights wφ ( f ) and wφ (g) are distinct. The weight of a face f under a k-labeling φ is the sum of labels carried by that face and all the edges and vertices incident with the face....

We prove Ramsey-type results for intersection graphs of geometric objects the plane. In particular, we prove the following bounds, all of which are tight apart from the constant c. There is a constant c > 0 such that for every family F of n ≥ 2 convex sets in the plane, the intersection graph of F or its complement contains a balanced complete bipartite graph of size at least cn. There is a con...

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular pyramid framework encode different types of relationships between regions. This paper compares different graph models used within the irregular pyramid frame...

A locally irregular graph is a graph whose adjacent vertices have distinct degrees. We say that a graph G can be decomposed into k locally irregular subgraphs if its edge set may be partitioned into k subsets each of which induces a locally irregular subgraph in G. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles an...

The concept of balanced decomposition number was introduced by Fujita and Nakamigawa in connection with a simultaneous transfer problem. A balanced colouring of a graph G is a pair (R,B) of disjoint subsets R,B ⊆ V (G) with |R| = |B|. A balanced decomposition D of a balanced colouring C = (R,B) of G is a partition of vertices V (G) = V1 ∪ V2 ∪ . . . ∪ Vr such that G[Vi] is connected and |Vi ∩R|...

In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.