578 research outputs found
Regular spanning subgraphs of bipartite graphs of high minimum degree
Let G be a simple balanced bipartite graph on vertices, , and . If then it has a -regular spanning subgraph. The
statement is nearly tight.Comment: submitte
On embedding well-separable graphs
Call a simple graph of order well-separable, if by deleting a
separator set of size the leftover will have components of size at most
. We prove, that bounded degree well-separable spanning subgraphs are
easy to embed: for every and positive integer there exists
an such that if , for a well-separable
graph of order and
for a simple graph of order , then . We extend our result
to graphs with small band-width, too.Comment: 11 pages, submitted for publicatio
Embedding graphs having Ore-degree at most five
Let and be graphs on vertices, where is sufficiently large.
We prove that if has Ore-degree at most 5 and has minimum degree at
least then Comment: accepted for publication at SIAM J. Disc. Mat
Optimal Random Matchings, Tours, and Spanning Trees in Hierarchically Separated Trees
We derive tight bounds on the expected weights of several combinatorial
optimization problems for random point sets of size distributed among the
leaves of a balanced hierarchically separated tree. We consider {\it
monochromatic} and {\it bichromatic} versions of the minimum matching, minimum
spanning tree, and traveling salesman problems. We also present tight
concentration results for the monochromatic problems.Comment: 24 pages, to appear in TC
- …