Global cycle properties in graphs with large minimum clustering coefficient

The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices. A complete structural characterization of those locally connected graphs, with minimum clustering coefficient 1/2 and maximum degree at most 6, that are fully cycle extendable is given in terms of strongly induced subgraphs with given attachment sets. Moreover, it is shown that all locally connected graphs with minimum clustering coefficient 1/2 and maximum degree at most 6 are weakly pancyclic, thereby proving Ryjacek's conjecture for this class of locally connected graphs.Comment: 16 pages, two figure

Stimulation of the immune response in vivo by different nucleic acids

The number of haemolytic plaque forming cells (PFCs) in the spleens of normal mice could not be increased by the injection of nucleic acids. However, when nucleic acids were injected into mice simultaneously with a priming dose of 3 x 10⁶ sheep erythrocytes (SRBCs) an appreciable stimulatory effect was observed. The same dose of SRBCs did not result in an increase in PFCs when injected alone. Nucleic acids at a concentration of approximately 1.5 mg per mouse resulted in an optimal stimulation of the immune response. Treatment of the nucleic acids by ribonuclease and deoxyribonuclase essentially eliminated the stimulatory effect of the RNA and DNA respectively whereas incubation with trypsin did not. Administration of pure single stranded RNAs from the livers and spleens of both normal and immunized mice resulted in a greater increase in the number of PFCs than nucleic acids from other sources. The stimulation of PFCs by RNAs from immunized mice was slightly greater than by RNAs from non-immunized mice. The immune response was also activated if the nucleic acids and the priming dose of antigen were not injected simultaneously.The articles have been scanned in colour with a HP Scanjet 5590; 300dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format