Fast approximation schemes for K3, 3-minor-free or K5-minor-free graphs
نویسندگان
چکیده
منابع مشابه
Fast approximation schemes for K3, 3-minor-free or K5-minor-free graphs
As the class of graphs of bounded treewidth is of limited size, we need to solve NP-hard problems for wider classes of graphs than this class. Eppstein introduced a new concept which can be considered as a generalization of bounded treewidth. A graph G has locally bounded treewidth if for each vertex v of G, the treewidth of the subgraph of G induced on all vertices of distance at most r from v...
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We present a fixed parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of the K5 or K3,3 as a minor in time O(3 6 √ n). In fact, we present our algorithm for any H-minor-free graph where H is a single-crossing graph (can be drawn on the plane with at most one crossing) and obtain the algorithm for K3,3(K5)-minor-free graphs as a special case. As a...
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As the class of graphs of bounded treewidth is of limited size we need to solve NP hard problems for wider classes of graphs than this class Eppstein introduced a new concept which can be considered as a generalization of bounded treewidth A graph G has locally bounded treewidth if for each vertex v of G the treewidth of the subgraph of G induced on all vertices of distance at most r from v is ...
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We improve the running time of the general algorithmic technique known as Baker’s approach (1994) on H-minor-free graphs from O(n) to O(f(|H |)n) showing that it is fixed-parameter tractable w.r.t. the parameter |H |. The numerous applications include e.g. a 2-approximation for coloring and PTASes for various problems such as dominating set and max-cut, where we obtain similar improvements. On ...
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In this paper, we show that for any even integer t ≥ 4, every 3-connected graph with no K3,t-minor has a spanning tree whose maximum degree is at most t − 1. This result is a common generalization of the result by Barnette [1] and the one by Chen, Egawa, Kawarabayashi, Mohar and Ota [4].
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2001
ISSN: 1571-0653
DOI: 10.1016/s1571-0653(04)00379-8