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
Graph factors modulo k
β Scribed by Thomassen, Carsten
- Book ID
- 122138715
- Publisher
- Elsevier Science
- Year
- 2014
- Tongue
- English
- Weight
- 192 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
The existence of a function a(k) (where k is a natural number) is established such that the vertex set of any graph G of minimum degree at least a ( k ) has a decomposition A U B U C such that G(A) has minimum degree a t least k , each vertex of A is joined to at least k vertices of B, and no two ve
## Abstract A graph is representable modulo __n__ if its vertices can be labeled with distinct integers between 0 and __n__, the difference of the labels of two vertices being relatively prime to __n__ if and only if the vertices are adjacent. ErdΕs and Evans recently proved that every graph is rep