Three equivalent partial orders on graphs with real edge-weights drawn on a convex polygon

Authors:
Hiro Ito
Affiliations:
Department of Communications and Computer Engineering, School of Informatics, Kyoto University, Kyoto, Japan
Venue:
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Year:
2004

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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.