Minimum congestion spanning trees in planar graphs
نویسندگان
چکیده
منابع مشابه
Minimum congestion spanning trees in planar graphs
The main purpose of the paper is to develop an approach to evaluation or estimation of the spanning tree congestion of planar graphs. This approach is used to evaluate the spanning tree congestion of triangular grids.
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The first problem considered in this paper: is it possible to find upper estimates for the spanning tree congestion for bipartite graphs which are better than for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n 3 2 , where n is the number of vertices. The second problem is to estimate spanning tree congestion of rand...
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Given a graph G and a positive integer k, we want to nd k spanning trees on G, not necessarily disjoint, of minimum total weight, such that the weight of each edge is subject to a penalty function if it belongs to more than one tree. We present a polynomial time algorithm for this problem; the algorithm's complexity is quadratic in k. We also present two heuristics with complexity linear in k. ...
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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: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.11.016