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...
متن کاملRecognizing Members of the Tournament Equilibrium Set is NP-hard
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 ...
متن کاملLocating-dominating codes in cycles
The smallest cardinality of an r-locating-dominating code in a cycle Cn of length n is denoted by M r (Cn). In this paper, we prove that for any r ≥ 5 and n ≥ nr when nr is large enough (nr = O(r3)) we have n/3 ≤ M r (Cn) ≤ n/3 + 1 if n ≡ 3 (mod 6) and M r (Cn) = n/3 otherwise. Moreover, we determine the exact values of M 3 (Cn) and M 4 (Cn) for all n.
متن کاملDominating cycles in halin graphs
A cycle in a graph is dominating if every vertex lies at distance at most one from the cycle and a cycle is D-cycle if every edge is incident with a vertex of the cycle. In this paper, first we provide recursive formulae for finding a shortest dominating cycle in a Hahn graph; minor modifications can give formulae for finding a shortest D-cycle. Then, dominating cycles and D-cycles in a Halin g...
متن کاملDominating Cartesian Products of Cycles
Let y(G) be the domination number of a graph G and let G U H denote the Cartesian product of graphs G and H. We prove that y(X) = (nr= ,nr)/(2m + l), where X = C1 0 CZ 0 ... 0 C, and all nt = ICkIr 1 < k < m, are multiples of 2m + 1. The methods we use to prove this result immediately lead to an algorithm for finding minimum dominating sets of the considered graphs. Furthermore the domination n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computer Science and Cybernetics
سال: 2012
ISSN: 1813-9663,1813-9663
DOI: 10.15625/1813-9663/18/3/1583