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Hardness results and an Exact Exponential Algorithm for the . . .
, 2011
"... 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 nonsparse graph classes, while it was investigated for some sparse graph classes before. We prove that the ..."
Abstract

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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 nonsparse graph classes, while it was investigated for some sparse graph classes before. We prove that the problem is NPhard even for chain graphs and split graphs. To cope with the hardness of the problem, we present a fast (exponentialtime) exact algorithm that runs in O ∗ (2 n) time, where n denotes the number of vertices. Additionally, we present simple combinatorial lemmas, which yield a constantfactor approximation algorithm for cographs, and a lineartime algorithm for chordal cographs.
SPANNING TREE CONGESTION OF PLANAR GRAPHS
"... Abstract. 123 The paper is devoted to estimates of the spanning tree congestion for some planar graphs. The main results of the paper: (1) We almost determined (up to ±1) the maximal possible spanning tree congestion for planar graphs. ..."
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Abstract. 123 The paper is devoted to estimates of the spanning tree congestion for some planar graphs. The main results of the paper: (1) We almost determined (up to ±1) the maximal possible spanning tree congestion for planar graphs.