Biclique Coverings and the Chromatic Number
| dc.creator | Mubayi, Dhruv | |
| dc.creator | Vishwanathan, Sundar | |
| dc.date | 2009-03-17 | |
| dc.date.accessioned | 2026-07-07T12:53:33Z | |
| dc.date.available | 2026-07-07T12:53:33Z | |
| dc.description | Consider a graph $G$ with chromatic number $k$ and a collection of complete bipartite graphs, or bicliques, that cover the edges of $G$. We prove the following two results: \medskip \noindent $\bullet$ If the bicliques partition the edges of $G$, then their number is at least $2^{\sqrt{\log_2 k}}$. This is the first improvement of the easy lower bound of $\log_2 k$, while the Alon-Saks-Seymour conjecture states that this can be improved to $k-1$. \medskip \noindent $\bullet$ The sum of the orders of the bicliques is at least $(1-o(1))k\log_2 k$. This generalizes, in asymptotic form, a result of Katona and Szemerédi who proved that the minimum is $k\log_2 k$ when $G$ is a clique. | |
| dc.identifier | https://arxiv.org/abs/0903.3048 | |
| dc.identifier | http://arxiv.org/abs/0903.3048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223656 | |
| dc.subject | Combinatorics | |
| dc.subject | 05 | |
| dc.title | Biclique Coverings and the Chromatic Number | |
| dc.type | text |