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Bounded Number (bounded + number)
Selected AbstractsOn factors of 4-connected claw-free graphs,JOURNAL OF GRAPH THEORY, Issue 2 2001H. J. Broersma Abstract We consider the existence of several different kinds of factors in 4-connected claw-free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4-connected line graph is hamiltonian, i.e., has a connected 2-factor. Conjecture 2 (Matthews and Sumner): Every 4-connected claw-free graph is hamiltonian. We first show that Conjecture 2 is true within the class of hourglass-free graphs, i.e., graphs that do not contain an induced subgraph isomorphic to two triangles meeting in exactly one vertex. Next we show that a weaker form of Conjecture 2 is true, in which the conclusion is replaced by the conclusion that there exists a connected spanning subgraph in which each vertex has degree two or four. Finally we show that Conjectures 1 and 2 are equivalent to seemingly weaker conjectures in which the conclusion is replaced by the conclusion that there exists a spanning subgraph consisting of a bounded number of paths © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 125,136, 2001 [source] Intermediate Preferences and Behavioral Conformity in Large GamesJOURNAL OF PUBLIC ECONOMIC THEORY, Issue 1 2009GUILHERME CARMONA Motivated by Wooders, Cartwright, and Selten (2006), we consider games with a continuum of players and intermediate preferences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the same element of the partition play the same action. We then use this result to show that all sufficiently large, equicontinuous games with intermediate preferences have an approximate equilibrium with the same property. Our result on behavior conformity for large finite game generalizes Theorem 3 of Wooders et al. (2006) by allowing both a wider class of preferences and a more general attribute space. [source] On the L(h, k)-labeling of co-comparability graphs and circular-arc graphsNETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2009Tiziana Calamoneri Abstract Given two nonnegative integers h and k, an L(h, k)- labeling of a graph G = (V, E) is a map from V to a set of integer labels such that adjacent vertices receive labels at least h apart, while vertices at distance at most 2 receive labels at least k apart. The goal of the L(h, k)-labeling problem is to produce a legal labeling that minimizes the largest label used. Since the decision version of the L(h, k)-labeling problem is NP-complete, it is important to investigate classes of graphs for which the problem can be solved efficiently. Along this line of thought, in this article we deal with co-comparability graphs, its subclass of interval graphs, and circular-arc graphs. To the best of our knowledge, ours is the first reported result concerning the L(h, k)-labeling of co-comparability and circular-arc graphs. In particular, we provide the first algorithm to L(h, k)-label co-comparability, interval, and circular-arc graphs with a bounded number of colors. Finally, in the special case where k = 1 and G is an interval graph, our algorithm improves on the best previously-known ones using a number of colors that is at most twice the optimum. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009 [source] APPROXIMATION PROPERTIES OF TP MODEL FORMS AND ITS CONSEQUENCES TO TPDC DESIGN FRAMEWORKASIAN JOURNAL OF CONTROL, Issue 3 2007Domonkos Tikk ABSTRACT Tensor Product Distributed Compensation (TPDC) is a recently established controller design framework, that links TP model transformation and Parallel Distributed Compensation (PDC) framework. TP model transformation converts different models to a common representational form: the TP model form. The primary aim of this paper is to investigate the approximation capabilities of TP model forms, because the universal applicability of TPDC framework strongly relies on it. We point out that the set of functions that can be approximated arbitrarily well by TP forms with bounded number of components lies no-where dense in the set of continuous functions. Consequently, in a class of control problems this property necessitates the usage of tradeoff techniques between the accuracy and the complexity of the TP form, which is easily feasible within the TPDC framework unlike in analytic models. [source] | ||||||||||