Regularity via topology of the lcm-lattice for $C_4$-free graphs

Details Regularity via topology of the lcm-lattice for $C_4$-free graphs Regularity via topology of the lcm-lattice for $C_4$-free graphs

2009-09-15

arxiv.org/abs/0909.2801v1

Mathematics

Combinatorics

14 pages

Scientific paper

We study the topology of the lcm-lattice of edge ideals and derive upper bounds on the Castelnuovo-Mumford regularity of the ideals. In this context it is natural to restrict to the family of graphs with no induced 4-cycle in their complement. Using the above method we obtain sharp upper bounds on the regularity when the complement is a chordal graph, or a cycle, or when the primal graph is claw free with no induced 4-cycle in its complement. For the later family we show that the second power of the edge ideal has a linear resolution.

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