Generation of cubic graphs

We describe a new algorithm for the efficient generation of all non-isomorphic connected cubic graphs. Our implementation of this algorithm is more than 4 times faster than previous generators. The generation can also be efficiently restricted to cubic graphs with girth at least 4 or 5

The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

The mysterious spin gap in high-temperature superconductors: New NMR/NQR studies

We review work, done mainly at the author's laboratory, on the spin gap which is the NMR manifestation of the pseudogap observed in the normal state of high-temperature superconductors. The relation of the spin gap to an electronic crossover in YBa2Cu4O8 is discussed. A possible explanation of both effects by assuming a charge density wave transition is presented. This suggestion is supported by measuring the isotope dependence of the spin gap in YBa2Cu4O

Spin-lattice relaxation in cuprate superconductors

This presentation gives a personal review of nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spin-lattice relaxation studies in cuprate superconductors mainly dealing with the YBa2Cu4O8 compound with many examples from the Zürich laboratory. The studies were performed in both the normal and the superconducting state with various NMR isotopes (e.g.,17O,63,65Cu,135,137Ba). The relatively broad signals were mostly obtained by a phase-alternating add-subtract spin-echo technique. We will discuss the general behavior of spin-lattice relaxation in the normal state and the calculation of the dynamic spin including an approach (on the basis of thet-J model) to calculate the relaxation for plane copper, oxygen, and yttrium. An application of the Luttingerliquid model to the relaxation of chain copper in YBa2Cu3O7 and YBa2Cu4O8 is also given. We then will deal with characteristic features of the YBa2Cu4O8 structure: the spin gap, an electronic crossover in the normal state, the single-spin fluid model, and the d-wave pairin

Halos around edge-on disk galaxies in the SDSS

We present a statistical analysis of halo emission for a sample of 1047 edge-on disk galaxies imaged in five bands by the Sloan Digital Sky Survey (SDSS). Stacking the homogeneously rescaled images of the galaxies, we can measure surface brightnesses as deep as mu_r~31 mag/arcsec^2. The results strongly support the almost ubiquitous presence of stellar halos around disk galaxies, whose spatial distribution is well described by a power-law $\rho\propto r^{-3}$, in a moderately flattened spheroid (c/a~0.6). The colour estimates in g-r and r-i, although uncertain, give a clear indication for extremely red stellar populations, hinting at old ages and/or non-negligible metal enrichment. These results support the idea of halos being assembled via early merging of satellite galaxies.Comment: 15 pages, 9 figures. Accepted for publication on MNRAS. Version with full resolution images available at http://www.mpa-garching.mpg.de/~zibetti/papers/halos_edgeon.pd

Spin pseudo-gap and interplane coupling in Y_2Ba_4Cu_7O_{15}: a ^{63}Cu nuclear spin-spin relaxation study

We report measurements of the Gaussian contribution, T_{2G}, to the plane ^{63}Cu nuclear spin--spin relaxation time in the YBa_2Cu_3O_7 and YBa_2Cu_4O_8 blocks of normal and superconducting Y_2Ba_4Cu_7O_{15}. The data confirm our previous results that adjacent CuO_2 planes have different doping levels and that these planes are strongly coupled. -- The static spin susceptibility at the anti-ferromagnetic wave vector exhibits a Curie--Weiss like temperature dependence in the normal state. -- The Y_2Ba_4Cu_7O_{15} data are incompatible with a phase diagram based on a single CuO_2 plane theory and suggest that the appearance of a spin gap implies interplane coupling. Additional data for YBa_2Cu_4O_8 and YBa_2Cu_3O_{6.982} are in accord with the single plane theory. -- The temperature dependence of T_{2G,ind} below T_c excludes isotropic s-wave superconductivity in all three compounds.Comment: 7 pages, REVTEX 3.0, 5 figures available upon reques

Interaction-assisted propagation of Coulomb-correlated electron-hole pairs in disordered semiconductors

A two-band model of a disordered semiconductor is used to analyze dynamical interaction induced weakening of localization in a system that is accessible to experimental verification. The results show a dependence on the sign of the two-particle interaction and on the optical excitation energy of the Coulomb-correlated electron-hole pair.Comment: 4 pages and 3 ps figure

Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697