Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649003 | Discrete Mathematics | 2010 | 7 Pages |
Abstract
We introduce a conjecture about constructing critically (s+1)(s+1)-chromatic graphs from critically ss-chromatic graphs. We then show how this conjecture implies that any unmixed height two square-free monomial ideal II in a polynomial ring RR, i.e., the cover ideal of a finite simple graph, has the persistence property, that is, Ass(R/Is)⊆Ass(R/Is+1) for all s≥1s≥1. To support our conjecture, we prove that the statement is true if we also assume that χf(G)χf(G), the fractional chromatic number of the graph GG, satisfies χ(G)−1<χf(G)≤χ(G)χ(G)−1<χf(G)≤χ(G). We give an algebraic proof of this result.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Christopher A. Francisco, Huy Tài Hà, Adam Van Tuyl,