E-resources
Peer reviewed
Open access
-
Bohman, Tom; Hofstad, Jakob
Journal of combinatorial theory. Series B, 20/May , Volume: 166Journal Article
The biclique partition number of a graph G=(V,E), denoted bp(G), is the minimum number of pairwise edge disjoint complete bipartite subgraphs of G so that each edge of G belongs to exactly one of them. It is easy to see that bp(G)≤n−α(G), where α(G) is the maximum size of an independent set of G. Erdős conjectured in the 80's that for almost every graph G equality holds; i.e., if G=Gn,1/2 then bp(G)=n−α(G) with high probability. Alon showed that this is false. We show that the conjecture of Erdős is true if we instead take G=Gn,p, where p is constant and less than a certain threshold value p0≈0.312. This verifies a conjecture of Chung and Peng for these values of p. We also show that if p0<p<1/2 then bp(Gn,p)=n−(1+Θ(1))α(Gn,p) with high probability.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.