Abstract
We extend a theorem of Villareal on bipartite graphs to the class of all graphs. On the way to this result, we study the basic covers algebra Ā(G) of an arbitrary graph G. We characterize with purely combinatorial methods the cases when 1) Ā(G) is a domain and 2) G is unmixed and Ā(G) is a domain.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2260-2267 |
| Number of pages | 8 |
| Journal | Communications in Algebra |
| Volume | 39 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 1 2011 |
| Externally published | Yes |
Keywords
- Basic covers
- Minimal vertex covers
- Symbolic powers
- Unmixed graphs
ASJC Scopus subject areas
- Algebra and Number Theory
Fingerprint Dive into the research topics of 'Unmixed graphs that are domains'. Together they form a unique fingerprint.
Cite this
Benedetti, B., & Varbaro, M. (2011). Unmixed graphs that are domains. Communications in Algebra, 39(7), 2260-2267. https://doi.org/10.1080/00927872.2010.519363