Extremal Subgraphs of Random Graphs: an Extended Version

Mathematics – Probability

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

36 pages, 2 figures

Scientific paper

We prove that there is a constant $c >0$, such that whenever $p \ge n^{-c}$, with probability tending to 1 when $n$ goes to infinity, every maximum triangle-free subgraph of the random graph $G_{n,p}$ is bipartite. This answers a question of Babai, Simonovits and Spencer (Journal of Graph Theory, 1990). The proof is based on a tool of independent interest: we show, for instance, that the maximum cut of almost all graphs with $M$ edges, where $M >> n$, is ``nearly unique''. More precisely, given a maximum cut $C$ of $G_{n,M}$, we can obtain all maximum cuts by moving at most $O(\sqrt{n^3/M})$ vertices between the parts of $C$.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Extremal Subgraphs of Random Graphs: an Extended Version 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 Extremal Subgraphs of Random Graphs: an Extended Version, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extremal Subgraphs of Random Graphs: an Extended Version will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-624136

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.