Geodesic
Hardness Results and an Exact Exponential Algorithm for the Spanning Tree Congestion Problem
Journal of Graph Algorithms and Applications, Tome 15 (2011) no. 6, pp. 727-751.

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Spanning tree congestion is a relatively new graph parameter, which has been studied intensively. This paper studies the complexity of the problem to determine the spanning tree congestion for non-sparse graph classes, while it was investigated for some sparse graph classes before. We prove that the problem is NP-hard even for chain graphs and split graphs. To cope with the hardness of the problem, we present a fast (exponential-time) exact algorithm that runs in O∗(2n) time, where n denotes the number of vertices. Additionally, we present simple combinatorial lemmas, which yield a constant-factor approximation algorithm for cographs, and a linear-time algorithm for chordal cographs.
DOI : 10.7155/jgaa.00246
Keywords: spanning tree congestion, NP-hardness, exact exponential algorithm, graph class 
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Yoshio Okamoto; Yota Otachi; Ryuhei Uehara; Takeaki Uno. Hardness Results and an Exact Exponential Algorithm for the Spanning Tree Congestion Problem. Journal of Graph Algorithms and Applications, Tome 15 (2011) no. 6, pp. 727-751. doi : 10.7155/jgaa.00246. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00246/

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