Chinese Postman Problem on Edge-Colored Multigraphs
Gregory Gutin, Mark Jones, Bin Sheng, Magnus Wahlstr\"om, Anders Yeo
TL;DR
This paper extends the polynomial-time solvability of the Chinese postman problem to edge-colored multigraphs, contrasting with its NP-hardness on mixed graphs, thus broadening the understanding of graph classes where the problem is tractable.
Contribution
The paper proves that the Chinese postman problem remains polynomial-time solvable on edge-colored multigraphs, unlike on mixed graphs where it is NP-hard.
Findings
Polynomial-time algorithm for edge-colored multigraphs
Contrast with NP-hardness on mixed graphs
Broader class of graphs with tractable Chinese postman problem
Abstract
It is well-known that the Chinese postman problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese postman problem on mixed graphs, i.e., graphs with directed and undirected edges, for which the problem is NP-hard.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Graph Labeling and Dimension Problems