Low diameter graph decompositions
โ Scribed by Nathan Linial; Michael Saks
- Publisher
- Springer-Verlag
- Year
- 1993
- Tongue
- English
- Weight
- 916 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We prove the following conjecture of A. Frank (Fifth British Combinatorial Conference, Aberdeen, Scotland, 1975): Let \(G\) be a connected simple graph of order \(n\), and \(n=n_{1}+\cdots+n_{k}\) be a partition of \(n\) with \(n_{i} \geqslant 2\). Suppose that the minimum degree of \(G\) is at leas
We prove that, for every integer k >~ 2, every graph has an edge-partition into 5k 2 log k sets, each of which is the edge-set of a graph with all degrees congruent to 1 mod k. This answers a question of Pyber. Pyber proved that every graph G has an edge-partition into four sets, each of which is