Parameterized Complexity of the Spanning Tree Congestion Problem
نویسندگان
چکیده
منابع مشابه
Complexity Results for the Spanning Tree Congestion Problem
We study the problem of determining the spanning tree congestion of a graph. We present some sharp contrasts in the complexity of this problem. First, we show that for every fixed k and d the problem to determine whether a given graph has spanning tree congestion at most k can be solved in linear time for graphs of degree at most d. In contrast, if we allow only one vertex of unbounded degree, ...
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We prove that every connected graph G of order n has a spanning tree T such that for every edge e of T the edge-cut defined in G by the vertex sets of the two components of T − e contains at most n 32 many edges which solves a problem posed by Ostrovskii (Minimal congestion trees, Discrete Math. 285 (2004), 219-226.)
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The linear or cyclic cutwidth of a graph G is the minimum congestion when G is embedded into either a path or a cycle respectively. A graph is cutwith critical if it is homeomorphically minimal and all of its subgraphs have lower cutwitdth. Our purpose is to extend the study of congestion critical graphs to embeddings on spanning trees.
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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. (2) The value of congestion indicator introduced in Ostrovskii [Discrete Math. 310 (2010), no. 6–7, 1204–1209] can be very far from the value of the spanning tree congestion. ...
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ژورنال
عنوان ژورنال: Algorithmica
سال: 2011
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-011-9565-7