In this paper, we consider a map labeling problem to maximize the number of independent labels in the plane. We first investigate the point labeling model that each label can be placed on a given set of anchors on a horizontal line. It is known that most of the map labeling decision models on a single line (horizontal or slope line) can be easily solved. However, the label number maximization m...

2 . The invariance principle . We first prove the following : If the theorem can be established for one particular sequence of independent random variables Y1, Y2, . . . satisfying the conditions of the theorem then the conclusion of the theorem holds for all sequences of independent random variables which satisfy the conditions of the theorem . In other words, if the limiting distribution exis...

A Turán connected graph TCn,α is obtained from α cliques of size b αc or d αe by joining all cliques by an edge to one central vertex in one of the larger cliques. The graph TCn,α was shown recently by Bruyère and Mélot to maximise the number of independent sets among connected graphs of order n and independence number α. We prove a generalisation of this result by showing that TCn,α in fact ma...

This paper is devoted to the proof of the surprising fact that almost all trees have an even number of independent vertex subsets (in the sense that the proportion of those trees with an odd number of independent sets tends to 0 as the number of vertices approaches ∞) and to its generalisation to other moduli: for fixed m, the probability that a randomly chosen tree on n vertices has a number o...

Let Gm,n be the m×n grid graph. That is, the vertices of Gm,n are the (m+1)(n+1) points (i, j) (0 ≤ i ≤ m, 0 ≤ j ≤ n) in the plane, and its edges are all of the pairs (i, j), (i′, j′) of vertices for which |i − i′| + |j − j′| = 1. Let f(m,n) be the number of independent sets of vertices in Gm,n. We study the growth of f(m,n). The figure below shows an independent set S in G4,6. figure=grid.eps ...

In a recent paper [l] K . CORRÁDI and A. HAJNAL proved that if a finite graph without multiple edges contains at least 3k vertices and the valency of every vertex is at least 2k, where k is a positive integer, then the graph contains k independent circuits, i . e . the graph contains as a subgraph a set of k circuits no two of which have a vertex in common . The present paper contains extension...

Let G be a (simple, undirected, finite) graph. A set S ⊆ V (G) is independent if no edge of G has both its endpoints in S. An independent set S is maximal if no independent set of G properly contains S. Let MIS(G) be the set of all maximal independent sets in G. Miller and Muller (1960) and Moon and Moser (1965) independently proved that the maximum, taken over all n-vertex graphs G, of |MIS(G)...

We describe fully polynomial time approximation schemes for various multicommodity ow problems in graphs with m edges and n vertices. We present the rst approximation scheme for maximum multicommodity ow that is independent of the number of commodities k, and our algorithm improves upon the runtime of previous algorithms by this factor of k, performing in O (?2 m 2) time. For maximum concurrent...

1. Introduction Estimating the number of sources provides useful information for signal processing applications, such as blind source separation (BSS) in the frequency domain [1]. It is well known that the number of dominant eigenvalues of the spatial correlation matrix corresponds to the number of sources [2,3]. However, it is difficult to distinguish dominant eigenvalues from the other eigenv...

In this paper an upper bound for the number of algebraically independent Poincaré-Liapunov constants in a certain basis for planar polynomial differential systems is given. Finally, it is conjectured that an upper bound for the number of functionally independent Poincaré-Liapunov quantities would be m + 3m− 7 where m is the degree of the polynomial differential system. Moreover, the computation...