## Abstract Chung defined a pebbling move on a graph __G__ to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number of a connected graph is the smallest number __f__(__G__) such that any distribution of __f__(__G__) pebbles on __G__
Graham’s pebbling conjecture on products of many cycles
✍ Scribed by David S. Herscovici
- Book ID
- 108113981
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 703 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
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## Abstract Given positive integers __n__ and __k__, let __g__~__k__~(__n__) denote the maximum number of edges of a graph on __n__ vertices that does not contain a cycle with __k__ chords incident to a vertex on the cycle. Bollobás conjectured as an exercise in [2, p. 398, Problem 13] that there e
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