Name
Title | ||
|---|---|---|
A conjecture on critical graphs and connections to the persistence of associated primes |
Abstract | ||
|---|---|---|
We introduce a conjecture about constructing critically (s+1)-chromatic graphs from critically s-chromatic graphs. We then show how this conjecture implies that any unmixed height two square-free monomial ideal I in a polynomial ring R, i.e., the cover ideal of a finite simple graph, has the persistence property, that is, Ass(R/I^s)@?Ass(R/I^s^+^1) for all s=1. To support our conjecture, we prove that the statement is true if we also assume that @g\"f(G), the fractional chromatic number of the graph G, satisfies @g(G)-1 |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.disc.2010.04.014 | Discrete Mathematics |
Keywords | Field | DocType |
monomial ideals,2010. 1,. associated primes,associated primes,monomial ideals. version: april 19,satisfiability | Discrete mathematics,Graph,Combinatorics,Algebraic number,Polynomial ring,Lonely runner conjecture,Monomial ideal,Conjecture,Critical graph,Mathematics | Journal |
Volume | Issue | ISSN |
310 | 15-16 | Discrete Mathematics |
Citations | PageRank | References |
2 | 0.91 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christopher A. Francisco | 1 | 9 | 2.62 |
| Huy Tài Hà | 2 | 11 | 3.96 |
| Adam Van Tuyl | 3 | 15 | 4.32 |