If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we...If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.展开更多
The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit desi...The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.展开更多
文摘If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.
文摘The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.
