Strong chromatic index of sparse graphs

A coloring of the edges of a graph $G$ is strong if each color class is an induced matching of $G$. The strong chromatic index of $G$, denoted by $\chi_{s}^{\prime}(G)$, is the least number of colors in a strong edge coloring of $G$. In this note we prove that $\chi_{s}^{\prime}(G)\leq (4k-1)\Delta (G)-k(2k+1)+1$ for every $k$-degenerate graph $G$. This confirms the strong version of conjecture stated recently by Chang and Narayanan [3]. Our approach allows also to improve the upper bound from [3] for chordless graphs. We get that $$ for any chordless graph $G$. Both bounds remain valid for the list version of the strong edge coloring of these graphs

Structural Transitions and Magnetic Structure in NH4CuCl3 via 14N-NMR

We report results of 14N-NMR experiments on NH4CuCl3 at the magnetic field of 7 T, where the 1/4-magnetization plateau is observed at low temperatures. The quadrupole splitting parameter $\nu_{z}$ splits below 70 K, indicating a structural phase transition. At 4.2 K, eight N sites with distinct values of both $\nu_{z}$ and the magnetic hyperfine shift $K_{z}$ are resolved in the NMR spectrum for general field directions. We then conlude that the magnetic structure in the 1/4-plateau does not break the symmetry of the crystal. Based on the NMR and the recent neutron scattering results by Ruegg et al. [Phys. Rev. Lett. 93 (2004) 037207], we propose that triplet dimers in the 1/4-plateau is formed not between the nearest neighbor pairs but over different chains.Comment: 7 pages, 5 figures, Proceedings for the International Symposium on Quantum Spin Systems, submitted to Prog. Theor. Phys. Author chang

Upper limits on electric dipole moments of tau-lepton, heavy quarks, and W-boson

We discuss upper limits on the electric dipole moments (EDM) of the tau-lepton, heavy quarks, and W-boson, which follow from the precision measurements of the electron and neutron EDM.Comment: 8 pages, 7 figures; misprint corrected, results do not chang