The Realizable Extension Problem and the Weighted Graph (K_3,3,l)

2010/09/28 by Jonathan McLaughlin, McLaughlin, Jonathan
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Structural Analysis and Optimization #cs.DM #math.AG

paper · pdf · doi:10.48550/arxiv.1009.5626

15 pages, 14 figures

arxiv created 2010/09/28 · openalex publication_date 2010/09/28 · arxiv updated 2010/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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