Making triangulations 4-connected using flips

We show that any combinatorial triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 9)/5) edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4-connected, showing that our bound is tight. In addition, for n >= 19, we improve the upper bound on the number of flips required to transform any 4-connected triangulation into the canonical triangulation (the triangulation with two dominant vertices), matching the known lower bound of 2n - 15. Our results imply a new upper bound on the diameter of the flip graph of 5.2n - 33.6, improving on the previous best known bound of 6n - 30.Comment: 22 pages, 8 figures. Accepted to CGTA special issue for CCCG 2011. Conference version available at http://2011.cccg.ca/PDFschedule/papers/paper34.pd

B_d mixing and prospects for B_s mixing at D0

Measurement of the B_s oscillation frequency via B_s mixing analyses provides a powerful constraint on the CKM matrix elements. The study of B_d oscillations is an important step towards B_s mixing and a preliminary measurement of Delta m_d has been made with ~250 pb^-1 of data collected with the upgraded Run II D0 detector. Different flavor tagging algorithms have been developed and are being optimized for use on a large set of B_s mesons that have been reconstructed in different semileptonic decay modes.Comment: Poster presented at the XXIV Physics in Collisions Conference (PIC04), Boston, USA, June 2004, 4 pages, LaTeX, 2 eps figure