2013/02/13 by Türker Bı́yı́koğlu, Turker Biyikoglu, Biyikoglu, Turker +2 · 1 citation
Mathematics · #05E40 #13F55 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #math.AC #math.AT #math.CO #msc:05E40 #msc:13F55
paper · pdf · doi:10.48550/arxiv.1302.3064
arxiv created 2013/02/13 · openalex publication_date 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.