3,426 research outputs found
Independent sets and cuts in large-girth regular graphs
We present a local algorithm producing an independent set of expected size
on large-girth 3-regular graphs and on large-girth
4-regular graphs. We also construct a cut (or bisection or bipartite subgraph)
with edges on large-girth 3-regular graphs. These decrease the gaps
between the best known upper and lower bounds from to , from
to and from to , respectively. We are using
local algorithms, therefore, the method also provides upper bounds for the
fractional coloring numbers of and and fractional edge coloring number . Our algorithms are applications of the technique introduced by Hoppen
and Wormald
- …