Mathematics

Estimates of multiplicity of irreducible multitours of some binary trees

O. S. Shcherbakov

Bauman Moscow State Technical University

Abstract: Irreducible multitours of binary trees appear in the weight formula for minimal fillings of finite metric spaces. In this paper, it is proved that the multiplicity of an irreducible multitour does not exceed 2 for any binary tree with 3 moustaches, and that it does not exceed 4 for binary trees consisting of four so-called sprouts.

Key words: finite metric space, minimal filling, multi-torus.

UDC: 515.124.4+519.175

Received: 15.09.2023

DOI: 10.55959/MSU0579-9368-1-66-2-2

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2025, 80:2, 89–96

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