It is conjectured by Erdős, Graham and Spencer that if 1 a 1 a 2 • • • a s with s i=1 1/a i < n -1/30, then this sum can be decomposed into n parts so that all partial sums are 1. This is not true for s i=1 1/a i = n -1/30 as shown by In 1997, Sándor proved that Erdős-Graham-Spencer conjecture is t
On a bound of Graham and Spencer for a graph-coloring constant
✍ Scribed by Robert W Irving
- Book ID
- 107884007
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 203 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract The distance coloring number __X__~__d__~(__G__) of a graph __G__ is the minimum number __n__ such that every vertex of __G__ can be assigned a natural number __m__ ≤ __n__ and no two vertices at distance __i__ are both assigned __i__. It is proved that for any natural number __n__ ther
## Abstract A graph __G__ is degree‐bounded‐colorable (briefly, db‐colorable) if it can be properly vertex‐colored with colors 1,2, …, k ≤ Δ(__G__) such that each vertex __v__ is assigned a color __c__(__v__) ≤ __v__. We first prove that if a connected graph __G__ has a block which is neither a com
Wallis, W.D. and G.-H. Zhang, On the partition and coloring of a graph by cliques, Discrete Mathematics 120 (1993) 191-203. We first introduce the concept of the k-chromatic index of a graph, and then discuss some of its properties. A characterization of the clique partition number of the graph G V