Planar Manhattan local minimal and critical networks

Alexandr O. Ivanov, Hông Vân Lê, and Alexey A. Tuzhilin

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Submission date: 06. Jul. 1999
Pages: 60
published in: European journal of combinatorics, 23 (2002) 8, p. 949-967 
DOI number (of the published article): 10.1006/eujc.2001.0561
Bibtex

Abstract:
The present work is devoted to the investigation of branching extremals, i.e., extremal networks, of the Manhattan length functional. Recall that the Manhattan length of a straight segment in is defined as the sum of the lengths of the segment projections to the Cartesian coordinate axis. It turns out that in the case of Manhattan length functional the class of local minimal networks is wider than the one of critical networks. The main aim of the present work is to describe the difference between these classes.