A graph G is (k+1)-critical if it is not k-colourable but G−e is k-colourable for any edge e ∈ E(G). In this paper we show that for any integers k ≥ 3 and l ≥ 5 there exists a constant c = c(k, l) > 0, such that for all ñ, there exists a (k + 1)-critical graph G on n vertices with n > ñ and odd girth at least l, which can be made (k − 1)-colourable only by the omission of at least cn2 edges.

The Acetaldimine-Vinylamine tautomeric system has been studied by employing the MNDO semiempirical method. The imine structure was found to be energetically favorable, as indicated by the calculated heats of formation, Gibbs free energy, LUMO and HOMO, and charges. The substitution of F, Cl, CN, CH3, CF3, NO2 and BH2 at the α-position was found to affect the geometrical parameters. F and Cl sub...

This study addresses the problem of identifying the large-scale topology of gene regulation networks from features that can be derived from microarray data sets. Understanding large-scale structures of gene regulation is fundamentally important in biology. Recent analysis of network properties of known biological networks has shown that they display scale-free features, but it is not yet clear ...

We introduce the problem of cluster-grouping and show that it integrates several important data mining tasks, i.e. subgroup discovery, mining correlated patterns and aspects from clustering. The problem of cluster-grouping can be regarded as a new type of inductive optimization query that asks for the k best patterns according to a convex criterion. The algorithm CG for solving cluster-grouping...

Data mining is the widely used research area in recent years. The results of data mining, represent relations in the data and are usually employed for classifying new data or for describing correlations hidden in the data. The process of classification predicts categorical labels based on the analysis of set of training data. Researchers have proposed many classification algorithms to automate ...

This study analyzes the effect of discretization on classification of datasets including continuous valued features. Six datasets from UCI which containing continuous valued features are discretized with entropy-based discretization method. The performance improvement between the dataset with original features and the dataset with discretized features is compared with k-nearest neighbors, Naive...

In this paper we review the applicability of representative inductive machine learning approaches in multicriteria decision making. We limit our review to four systems. We use SICLA and KBG as representative conceptual clustering systems and ID3 and CN2 as representative learning from examples systems. We demonstrate our results by way of two real world decision making exemplars. The first exem...

For an arbitrary matrix A of n×n symbols, consider its submatrices of size k×k, obtained by deleting n−k rows and n−k columns. Optionally, the deleted rows and columns can be selected symmetrically or independently. We consider the problem of whether these multisets determine matrix A. Following the ideas of Krasikov and Roditty in the reconstruction of sequences from subsequences, we replace t...

The covalent structure of the rat liver 60 S ribosomal subunit protein L37 was determined. Twenty-four tryptic peptides were purified and the sequence of each was established; they accounted for all 111 residues of L37. The sequence of the first 30 residues of L37, obtained previously by automated Edman degradation of the intact protein, provided the alignment of the first 9 tryptic peptides. T...