A Note on Graph Pebbling

Details A Note on Graph Pebbling A Note on Graph Pebbling

2004-06-03

arxiv.org/abs/math/0406053v1

Graphs and Combinatorics 18 (2002), 219--225

Mathematics

Combinatorics

12 pages

Scientific paper

We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let k(d) denote the least positive integer so that every graph G with diameter at most d and connectivity at least k(d) is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must satisfy k(d)=\Omega(2^d/d). In this note, we show that k exists and satisfies k(d)=O(2^{2d}). We also apply this result to improve the upper bound on the random graph threshold of the Class 0 property.

Affiliated with

Also associated with

No associations

Rating

A Note on Graph Pebbling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Note on Graph Pebbling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Note on Graph Pebbling will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-618287