Structural properties of 1-planar graphs and an application to acyclic edge coloring

A graph is called 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we establish a local property of 1-planar graphs which describes the structure in the neighborhood of small vertices (i.e. vertices of degree no more than seven). Meanwhile, some new classes of light graphs in 1-planar graphs with the bounded degree are found. Therefore, two open problems presented by Fabrici and Madaras [The structure of 1-planar graphs, Discrete Mathematics, 307, (2007), 854-865] are solved. Furthermore, we prove that each 1-planar graph $G$ with maximum degree $\Delta(G)$ is acyclically edge $L$-choosable where $L=\max\{2\Delta(G)-2,\Delta(G)+83\}$.Comment: Please cite this published article as: X. Zhang, G. Liu, J.-L. Wu. Structural properties of 1-planar graphs and an application to acyclic edge coloring. Scientia Sinica Mathematica, 2010, 40, 1025--103

A new potential radiosensitizer: ammonium persulfate modified WCNTs

Radiotherapy plays a very important role in cancer treatment. Radiosensitizers have been widely used to enhance the radiosensitivity of cancer cells at given radiations. Here we fabricate multi-walled carbon nanotubes with ammonium persulfate, and get very short samples with 30-50 nanometer length. Cell viability assay show that f-WCNTs induce cell death significantly. We hypothesize that free radicals originated from hydroxyl and carbonyl groups on the surface of f-WCNTs lead cell damage