Upper Bounds for the Regularity of Gap-Free Graphs in Terms of Minimal Triangulation

In this work, we show an upper bound for the regularity of edge ideals of gap-free graphs, in terms of their minimal triangulation. We prove that reg ( I ( G ) ) ≤ reg ( I ( C U ) ) , where C U is a 3-uniform clutter consists of certain 3-paths in a minimal triangulation of G . By using this, a gene...

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Bibliographic Details
Published inInternational journal of applied and computational mathematics Vol. 7; no. 6
Main Authors Nandi, Rimpa, Nanduri, Ramakrishna
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.12.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Applied mathematics
Clutter
Computational mathematics
Computational Science and Engineering
Graphs
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Regularity
Theoretical
Triangulation
Upper bounds
05E40
Gap-free graph
Path ideal
Regularity
05E99
13D02
13F55
Minimal triangulation
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Summary:In this work, we show an upper bound for the regularity of edge ideals of gap-free graphs, in terms of their minimal triangulation. We prove that reg ( I ( G ) ) ≤ reg ( I ( C U ) ) , where C U is a 3-uniform clutter consists of certain 3-paths in a minimal triangulation of G . By using this, a general upper bound for the regularity of gap-free graphs are studied. If H is the 3-uniform clutter consists of certain 3-cliques in G or in its triangulation and H is chordal, then reg ( I ( G ) ) ≤ 3 .
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-021-01156-6