DIMACS
DIMACS REU 2012

Hello! My name is Pavel Veselý and I'm one of the group from Czech republic. I come from Faculty of Mathematics and Physics, Charles University in Prague. I spend most of the day in the office 446 in CoRE building. Mentor of our Czech group is James Abello.

If you want to contact me via email, please write to pavelv (something) reu (another thing) dimacs.rutgers.edu.

Problems

We have recieved about ~4 topics from graph theory and probability and some problems in these topics.

My favourite is about peel numbers (or coreness). Given a graph, we start "peeling" (deleting) vertices with degree 1 interativelly. That means when we delete a vertex with degree 1 (and edges incident to it), there can occur new vertex of degree 1, which had degree 2 before. We also delete this vertex. All vertices deleted during the phase, when vertices with degree 1 or less are deleted, obtain peel number 1. And this is done again for degree 2 (giving peel number 2 to deleted vertices) as far as there is any vertex left.

There are several problems around that, like finding a set of operations that are preserving peel numbers and that are able to make a graph G from another graph H with the same peel numbers without changing the peel numbers during the process.