Geodesic
Associated primes of monomial ideals and odd holes in graphs
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 2, pp. 287-301.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $G$ be a finite simple graph with edge ideal $I( G)$. Let $I( G) ^{ \vee }$ denote the Alexander dual of $I( G)$. We show that a description of all induced cycles of odd length in $G$ is encoded in the associated primes of $( I( G) ^{ \vee }) ^{2}$. This result forms the basis for a method to detect odd induced cycles of a graph via ideal operations, e.g., intersections, products and colon operations. Moreover, we get a simple algebraic criterion for determining whether a graph is perfect. We also show how to determine the existence of odd holes in a graph from the value of the arithmetic degree of $( I( G) ^{ \vee }) ^{2}$.
Keywords: keywords edge ideals, odd cycles, perfect graphs, associated primes, arithmetic degree 
@article{JAC_2010__32_2_a0,
     author = {Francisco, Christopher A. and H\`a, Huy T\`ai and Van Tuyl, Adam},
     title = {Associated primes of monomial ideals and odd holes in graphs},
     journal = {Journal of Algebraic Combinatorics},
     pages = {287--301},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__32_2_a0/}
}
TY  - JOUR
AU  - Francisco, Christopher A.
AU  - Hà, Huy Tài
AU  - Van Tuyl, Adam
TI  - Associated primes of monomial ideals and odd holes in graphs
JO  - Journal of Algebraic Combinatorics
PY  - 2010
SP  - 287
EP  - 301
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2010__32_2_a0/
LA  - en
ID  - JAC_2010__32_2_a0
ER  - 
%0 Journal Article
%A Francisco, Christopher A.
%A Hà, Huy Tài
%A Van Tuyl, Adam
%T Associated primes of monomial ideals and odd holes in graphs
%J Journal of Algebraic Combinatorics
%D 2010
%P 287-301
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2010__32_2_a0/
%G en
%F JAC_2010__32_2_a0
Francisco, Christopher A.; Hà, Huy Tài; Van Tuyl, Adam. Associated primes of monomial ideals and odd holes in graphs. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 2, pp. 287-301. http://geodesic.mathdoc.fr/item/JAC_2010__32_2_a0/