43634604
Hamiltonian Kneser Graphs
The Kneser graph K(n,k) has as vertices the k-subsets of {1, 2, ..., n}. Two vertices are adjacent if the corresponding k-subsets are disjoint. It was recently proved by the first author [2] that Kneser graphs have Hamilton cycles for n >= 3k. In this note, we give a short proof for the case when k divides n.
33065239
Triangle-free Hamiltonian Kneser graphs
The Kneser graph K(n,k) has as vertices the k-subsets of {1, 2,...,n}. Two vertices are adjacent if the k-sets are disjoint. When n > 3k, the Kneser Graph K(n, k) has no triangle. In this paper, we prove that K(n,k) is Hamiltonian for n ≥ (3k + 1 + √5k2- 2k + 1)/2, and extend this to the bipartite Kneser graphs. Note that (3k + 1 + √5k2 - 2k + 1)/2 > 2.62k + 1.
15445426
An Ore-type Condition for Cyclability
A graph G is said to be cyclable if for each orientation D of G, there exists a set S(D) ?V(G) such that reversing all the arcs with one end in S results in a Hamiltonian digraph. Let G be a simple graph of even ordern? 8. In this paper, we show that if the degree sum of any two nonadjacent vertices is not less thann+ 1, then G is cyclable and the lower bound is sharp.
39700388
Surface Spatial Index Structure of High-Dimensional Space
This paper proposes a spatial index structure based on a new space-partitioning method. Previous research proposed various high dimensional index structures. However, when dimensionality becomes high, the effectiveness of the spatial index structure disappears. This problem is called the “curse of dimensionality”. This paper focuses on the fact that the volume of high dimensional space is mostly occupied by its surface and then proposes a new surface index structure. The utility of this new surface spatial index structure is illustrated through a series of experiments.
832740
Constrained genetic algorithms and their applications in nonlinear constrained optimization
The paper presents a problem-independent framework that unifies various mechanisms for solving discrete constrained nonlinear programming (NLP) problems whose functions are not necessarily differentiable and continuous. The framework is based on the first-order necessary and sufficient conditions in the theory of discrete constrained optimization using Lagrange multipliers. It implements the search for discrete-neighborhood saddle points (SP/sub dn/) by performing ascents in the original-variable subspace and descents in the Lagrange-multiplier subspace. Our study on the various mechanisms shows that CSAGA, a combined constrained simulated annealing and genetic algorithm, performs well. Finally, we apply iterative deepening to determine the optimal number of generations in CSAGA.
4357183
A New Proof of Wojcicka's Conjecture
A graph G is 3-domination-critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Wojcicka conjectured that every 3-domination-critical graph with δ ≥ 2 has a hamiltonian cycle (J. Graph Theory 14 (1990) 205-215). The conjecture had been proved and its proof consists of two parts: the case α ≤ δ + 1 (J. Graph Theory 25 (1997) 173-184) and the case α = δ + 2 (Discrete Appl. Math. 92 (1999) 57-70). In this paper, we give a new and simple proof of the conjecture by using Hanson's (J. Combin. Math. Combin. Comput. 13 (1993) 121-128) and Bondy-Chvatal's (Discrete Math. 15(1976) 111-135) closure operations.
17475296
Statistical geometrical features for texture classification
Abstract This paper proposes a novel set of 16 features based on the statistics of geometrical attributes of connected regions in a sequence of binary images obtained from a texture image. Systematic comparison using all the Brodatz textures shows that the new set achieves a higher correct classification rate than the well-known Statistical Gray Level Dependence Matrix method, the recently proposed Statistical Feature Matrix, and Liu's features. The deterioration in performance with the increase in the number of textures in the set is less with the new SGF features than with the other methods, indicating that SGF is capable of handling a larger texture population. The new method's performance under additive noise is also shown to be the best of the four.