منابع مشابه
Recognizing tough graphs is NP-hard
We consider only undirected graphs without loops or multiple edges. Our terminology and notation will be standard except as indicated; a good reference for any undefined terms is [2]. We will use c(G) to denote the number of components of a graph G. Chvtital introduced the notion of tough graphs in [3]. Let t be any positive real number. A graph G is said to be t-tough if tc(G-X)5 JXJ for all X...
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A recurring theme in the mathematical social sciences is how to select the “most desirable” elements given some binary dominance relation on a set of alternatives. Schwartz’s Tournament Equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context. Due to its unwieldy recursive definition, little is ...
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We show that it is NP-hard to determine if a cubic graph G is 1-tough. We then use this result to show that for any integer t ≥ 1, it is NP-hard to determine if a 3 t-regular graph is t-tough. We conclude with some remarks concerning the complexity of recognizing certain subclasses of tough graphs.
متن کاملThe complexity of recognizing minimally tough graphs
Let t be a positive real number. A graph is called t-tough, if the removal of any cutset S leaves at most |S|/t components. The toughness of a graph is the largest t for which the graph is t-tough. A graph is minimally t-tough, if the toughness of the graph is t and the deletion of any edge from the graph decreases the toughness. The complexity class DP is the set of all languages that can be e...
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We prove that computing a geometric minimum-dilation graph on a given set of points in the plane, using not more than a given number of edges, is an NP-hard problem, no matter if edge crossings are allowed or forbidden. We also show that the problem remains NP-hard even when a minimum-dilation tour or path is sought; not even an FPTAS exists in this case.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1990
ISSN: 0166-218X
DOI: 10.1016/0166-218x(90)90001-s