Bounding Castelnuovo-Mumford regularity of graphs via Lozin's transformation
Combinatorics
2013-02-14 v1 Commutative Algebra
Algebraic Topology
Abstract
We prove that when a Lozin's transformation is applied to a graph, the (Castelnuovo-Mumford) regularity of the graph increases exactly by one, as it happens to its induced matching number. As a consequence, we show that the regularity of a graph can be bounded from above by a function of its induced matching number. We also prove that the regularity of a graph is always less than or equal to the sum of its induced matching and decycling numbers.
Keywords
Cite
@article{arxiv.1302.3064,
title = {Bounding Castelnuovo-Mumford regularity of graphs via Lozin's transformation},
author = {Turker Biyikoglu and Yusuf Civan},
journal= {arXiv preprint arXiv:1302.3064},
year = {2013}
}