Criterion of irreducibility of multi-loop Feynman integrals

The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the p ossibility of such reduction for the given particular integral was unclear. The recently proposed technique for studying the recurrence relations as b y-product provides with simple criterion of the irreducibility. (C) 2000 Pu blished by Elsevier Science B.V. All rights reserved.