On The Chromatic Number Of Pentagon-Free Graphs Of Large Minimum Degree

We prove that, for each fixed real number c > 0, the pentagon-free graphs of minimum degree at least cn (where n is the number of vertices) have bounded chromatic number. This problem was raised by Erdős and Simonovits in 1973. A similar result holds for any other fixed odd cycle, except the triangle for which there is no such result for c<1/3.     

Highly connected non-2-linked digraphs

For every natural numberk there exists a stronglyk-connected digraph which contains two vertices through which there is no directed cycle.     

Physicochemical characterisation of different welding aerosols

Physicochemical properties important in exposure characterisation of four different welding aerosols were investigated. Particle number size distributions were determined by scanning mobility particle sizer (SMPS), mass size distributions by separation and weighing the individual size fractions of an 11-stage cascade impactor. The size distribution of the primary particles of agglomerates, chemical composition and morphology of the particles were examined by TEM. There were significant differences in the particle number size distributions of the different welding aerosols according to the SMPS determinations. The particle mass size distributions determined gravimetrically were, however, not really different. The dominant range with respect to mass was between 0.1 and 1 μm, regardless of the welding technique. Most of the primary particles in all different welding aerosols had diameters between 5 and 40 nm. All types of primary particles had a tendency to form chainlike agglomerates. A clear size dependence of the particle chemical composition was encountered in the case of manual metal arc welding aerosol. Small particles with diameters below 50 nm were mostly metal oxides in contrast to larger particles which also contained more volatile elements (e.g. potassium, fluorine, sodium, sulphur).     

Nowhere-zero 3-flows and modulo k-orientations

The main theorem of this paper provides partial results on some major open problems in graph theory, such as Tutte?s 3-flow conjecture (from the 1970s) that every 4-edge connected graph admits a nowhere-zero 3-flow, the conjecture of Jaeger, Linial, Payan and Tarsi (1992) that every 5-edge-connected graph is _Z3$Z_3$-connected, Jaeger?s circular flow conjecture (1984) that for every odd natural number k?3$k?3$, every (2k−2)$(2k-2)$-edge-connected graph has a modulo k  -orientation, etc. It was proved recently by Thomassen that, for every odd number k?3$k?3$, every (2k²+k)$(2k^2+k)$-edge-connected graph G has a modulo k-orientation; and every 8-edge-connected graph G   is _Z3$Z_3$-connected and admits therefore a nowhere-zero 3-flow. In the present paper, Thomassen?s method is refined to prove the following: For every odd number  k?3$k?3$, every  (3k−3)$(3k-3)$-edge-connected graph has a modulo k-orientation. As a special case of the main result, every 6-edge-connected graph is  _Z3$Z_3$-connected and admits therefore a nowhere-zero 3-flow. Note that it was proved by Kochol (2001) that it suffices to prove the 3-flow conjecture for 5-edge-connected graphs.     

Determination of aluminium in human biopsy and necropsy specimens by direct solid sampling cup-in-tube electrothermal atomic absorption spectrometry

Summary A method for the direct determination of aluminium in human biopsy and necropsy specimens is described. The working range of the procedure was from 0.2 to 100 mgkg^–1 using clean room facilities. The detection limit of aluminium is strongly dependent on the measures taken to reduce aluminium contamination during analysis. Expansion of the working range by a factor of five was possible by making use of the absorption due to sigma component when applying Zeeman-Effect background correction.     

On k-rails in graphs

A k-rail is the union of k paths each pair of which has exactly the endvertices in common. We first give a sufficient degree-condition for the existence of k-rails in graphs. Next we determine the number of edges required in 3-connected graphs to guarantee the existence of 5-rails, and finally we solve the corresponding problem for graphs with no prescribed connectivity.     

Cycles in graphs of uncountable chromatic number

We answer a question of Erdős [1], [2] by showing that any graph of uncountable chromatic number contains an edge through which there are cycles of all (but finitely many) lengths.