The Realizable Extension Problem and the Weighted Graph $(K_{3,3},l)$

Details The Realizable Extension Problem and the Weighted Graph $(K_{3,3},l)$ The Realizable Extension Problem and the Weighted Graph $(K_{3,3},l)$

2010-09-28

arxiv.org/abs/1009.5626v1

Mathematics

Algebraic Geometry

15 pages, 14 figures

Scientific paper

This note outlines the realizable extension problem for weighted graphs and provides results of a detailed analysis of this problem for the weighted graph $(K_{3,3},l)$. This analysis is then utilized to provide a result relating to the connectedness of the moduli space of planar realizations of $(K_{3,3},l)$. The note culminates with two examples which show that in general, realizability and connectedness results relating to the moduli spaces of weighted cycles which are contained in a larger weighted graph cannot be extended to similar results regarding the moduli space of the larger weighted graph.

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