Connectedness in graph limits

Details Connectedness in graph limits Connectedness in graph limits

2008-02-26

arxiv.org/abs/0802.3795v2

Mathematics

Combinatorics

21 pages. References added (v2)

Scientific paper

We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric functions on a probability space; there are natural definitions of direct sums and connectedness for such functions, and there is a perfect correspondence with the corresponding properties of the graph limit. Similarly, every graph limit determines an infinite random graph, which is a.s. connected if and only if the graph limit is connected. There are also characterizations in terms of the asymptotic size of the largest component in the corresponding finite random graphs, and of minimal cuts in sequences of graphs converging to a given limit.

Affiliated with

Also associated with

No associations

Rating

Connectedness in graph limits 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 Connectedness in graph limits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connectedness in graph limits will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-606886