The complexity of recognizing minimally tough graphs
نویسندگان
چکیده
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 expressed as the intersection of a language in NP and a language in coNP. We prove that recognizing minimally t-tough graphs is DP-complete for any positive integer t and for any positive rational number t ≤ 1/2.
منابع مشابه
The Complexity of Recognizing Tough Cubic Graphs
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 Toughness in Regular Graphs
Let t ≥ 1 be an integer. We show that it is NP-hard to determine if an r-regular graph is t-tough for any fixed integer r ≥ 3 t. We also discuss the complexity of recognizing if an r-regular graph is t-tough, for any rational t ≥ 1.
متن کاملRecognizing 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...
متن کاملVarious results on the toughness of graphs
Let G be a graph, and let t ≥ 0 be a real number. Then G is t-tough if tω(G − S) ≤ |S| for all S ⊆ V (G) with ω(G− S) > 1, where ω(G− S) denotes the number of components of G − S. The toughness of G, denoted by τ(G), is the maximum value of t for which G is t-tough (taking τ(Kn) = ∞ for all n ≥ 1). G is minimally t-tough if τ(G) = t and τ(H) < t for every proper spanning subgraph H of G. We dis...
متن کاملDegree-constrained spanning trees
S of the Ghent Graph Theory Workshop on Longest Paths and Longest Cycles Kathie Cameron Degree-constrained spanning trees 2 Jan Goedgebeur Finding minimal obstructions to graph coloring 3 Jochen Harant On longest cycles in essentially 4-connected planar graphs 3 Frantǐsek Kardoš Barnette was right: not only fullerene graphs are Hamiltonian 4 Gyula Y. Katona Complexity questions for minimally t-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1705.10570 شماره
صفحات -
تاریخ انتشار 2017