

Preprint 46/1999
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.