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) |
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Pages (from-to) | 2260-2267 |
Number of pages | 8 |
Journal | Communications in Algebra |
Volume | 39 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2011 |
Externally published | Yes |
Keywords
- Basic covers
- Minimal vertex covers
- Symbolic powers
- Unmixed graphs
ASJC Scopus subject areas
- Algebra and Number Theory