Let G be a multipartite multigraph without loops. Then G is said to be internally fair if its edges are shared as evenly as possible among all pairs of its partite sets. An internally fair factorization of G is an edge-decomposition of G into internally fair regular spanning subgraphs. A holey factor of G is a regular subgraph spanning all vertices but one partite set. An internally fair holey ...

Given graphs G and H , an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H . Let φH(n) be the smallest number φ such that any graph G of order n admits an H-decomposition with at most φ parts. Here we study the case when H = C7, that is, the cycle of length 7 and prove that φC7(n) = n/4 for all n ≥ 10.

Mesh generation and refinement are widely used in applications that require a decomposition of geometric objects for processing. Longest edge refinement algorithms seek to obtain a better decomposition over selected regions of the mesh by the division of its elements. Until now, these algorithms did not provide theoretical guarantees on the size of the triangulation obtained. In this paper we p...

-In this paper we use the parameteric polar representation to extend the application of edge directional information from circle to ellipse extraction. As a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub-spaces and one final histogram accumulator. The mapping includes the tangent of the angle of the first and second direc...

Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let φH(n) be the smallest number φ such that any graph G of order n admits an H-decomposition with at most φ parts. Here we determine the asymptotic of φH(n) for any fixed graph H as n tends to infinity. Partially supported by the Nation...

A decomposition of Kn \L, the complete graph of order n with a subgraph L (called the leave) removed, into edge disjoint copies of a graph G is called a maximum packing of Kn with G if L contains as few edges as possible. A decomposition of Kn U P, the complete graph union a graph P (called the padding), into edge disjoint copies of a graph G is called a minimum covering of Kn with G if P conta...

Abstract A digraph G is k - geodetic if for any pair of (not necessarily distinct) vertices $$u,v \in V(G)$$ u , v ∈ V ( G ) there at most one walk length $$\le k$$ <mm...

This paper suggests a new approach to edge extraction in terms of image decomposition and restoration, which adopts some specific edge extraction operator as seed operator to extract edge in a group of sub-images produced by sub-sampling original image and restoring the extracted edge-pixels to their corresponding positions in original image. It is a fast method to extract edge features at any ...

Given graphs H and G, we say that H has a G-Decomposition if we are to partition the edge set of H so that for each part P of the partition, the subgraph of H induced by P is isomorphic to G. Let I(D) be the intersection generated by such a decomposition. We say that D is an automorphic decomposition of H with respect to G if I(D) ∼= H. In this talk, we will show several examples of such a deco...

Given two graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let φ(n,H) be the smallest number φ such that any graph G of order n admits an H-decomposition with at most φ parts. Pikhurko and Sousa conjectured that φ(n,H) = ex(n,H) for χ(H) ≥ 3 and all sufficiently large n, where ex(n,H) denote...