Abstract
Three partial orders, cut-size order, length order, and operation order, defined between labeled multigraphs with the same order are known to be equivalent. This paper extends the result on edge-capacitated graphs, where the capacities are real numbers, and it presents a proof of the equivalence of the three relations. From this proof, it is also shown that we can determine whether or not a given graph precedes another given graph in polynomial time.
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Ito, H. (2005). Three Equivalent Partial Orders on Graphs with Real Edge-Weights Drawn on a Convex Polygon. In: Akiyama, J., Kano, M., Tan, X. (eds) Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol 3742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11589440_13
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DOI: https://doi.org/10.1007/11589440_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30467-8
Online ISBN: 978-3-540-32089-0
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