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The binomial edge ideal of a pair of graphs

Published online by Cambridge University Press:  11 January 2016

Viviana Ene ,
Jürgen Herzog ,
Takayuki Hibi  and
Ayesha Asloob Qureshi
Viviana Ene
Affiliation:
Faculty of Mathematics and Computer Science Ovidius University, 900527 Constanta, Romania, vivian@univ-ovidius.ro
Jürgen Herzog
Affiliation:
Fachbereich Mathematik Universität Duisburg-Essen, Campus Essen 45117 Essen, Germany, juergen.herzog@uni-essen.de
Takayuki Hibi
Affiliation:
Department of Pure and Applied Mathematics Graduate School of Information Science and Technology Osaka University, Toyonaka Osaka 560-0043, Japan, hibi@math.sci.osaka-u.ac.jp
Ayesha Asloob Qureshi
Affiliation:
Abdus Salam School of Mathematical Sciences GC University, New Muslim Town Lahore 54600, Pakistan, ayesqi@gmail.com
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Abstract

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We introduce a class of ideals generated by a set of 2-minors of an (m × n)-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gröbner basis and characterize unmixedness and Cohen–Macaulayness.

Keywords

13P1013C1313C1513P25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 213 , March 2014 , pp. 105 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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