Regular packings of regular graphs

Asymptotically Optimal Tree-Packings in Regular Graphs

Let T be a tree with t vertices. Clearly, an n vertex graph contains at most n/t vertex disjoint trees isomorphic to T . In this paper we show that for every > 0, there exists a D( , t) > 0 such that, if d > D( , t) and G is a simple d-regular graph on n vertices, then G contains at least (1− )n/t vertex disjoint trees isomorphic to T .

Regular Sphere Packings

A collection of non-overlapping spheres in the space is called a packing. Two spheres are said to be neighbours if they have a boundary point in common. A packing is called k-regular if each sphere has exactly k neighbours. We are concerned with the following question. What is the minimum number of not necessarily congruent spheres which may form a k-regular packing? In general, for which natur...

Regular Circle Packings

Ball packings with high chromatic numbers from strongly regular graphs

Inspired by Bondarenko’s counter-example to Borsuk’s conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers are significantly higher than the dimensions. In particular, from generalized quadrangles we obtain unit ball packings in dimension q3 − q2 + q with chromatic number q3 + 1, where q is a prime power. This improves the previous low...

OPTIMAL ANALYSIS OF NON-REGULAR GRAPHS USING THE RESULTS OF REGULAR MODELS VIA AN ITERATIVE METHOD

In this paper an efficient method is developed for the analysis of non-regular graphs which contain regular submodels. A model is called regular if it can be expressed as the product of two or three subgraphs. Efficient decomposition methods are available in the literature for the analysis of some classes of regular models. In the present method, for a non-regular model, first the nodes of the ...