Large rainbow matchings in large graphs

A \textit{rainbow subgraph} of an edge-colored graph is a subgraph whose edges have distinct colors. The \textit{color degree} of a vertex $v$ is the number of different colors on edges incident to $v$. We show that if $n$ is large enough (namely, $n\geq 4.25k^2$), then each $n$-vertex graph $G$ with minimum color degree at least $k$ contains a rainbow matching of size at least $k$

Grundy Coloring & Friends, Half-Graphs, Bicliques

The first-fit coloring is a heuristic that assigns to each vertex, arriving in a specified order ?, the smallest available color. The problem Grundy Coloring asks how many colors are needed for the most adversarial vertex ordering ?, i.e., the maximum number of colors that the first-fit coloring requires over all possible vertex orderings. Since its inception by Grundy in 1939, Grundy Coloring has been examined for its structural and algorithmic aspects. A brute-force f(k)n^{2^{k-1}}-time algorithm for Grundy Coloring on general graphs is not difficult to obtain, where k is the number of colors required by the most adversarial vertex ordering. It was asked several times whether the dependency on k in the exponent of n can be avoided or reduced, and its answer seemed elusive until now. We prove that Grundy Coloring is W[1]-hard and the brute-force algorithm is essentially optimal under the Exponential Time Hypothesis, thus settling this question by the negative. The key ingredient in our W[1]-hardness proof is to use so-called half-graphs as a building block to transmit a color from one vertex to another. Leveraging the half-graphs, we also prove that b-Chromatic Core is W[1]-hard, whose parameterized complexity was posed as an open question by Panolan et al. [JCSS \u2717]. A natural follow-up question is, how the parameterized complexity changes in the absence of (large) half-graphs. We establish fixed-parameter tractability on K_{t,t}-free graphs for b-Chromatic Core and Partial Grundy Coloring, making a step toward answering this question. The key combinatorial lemma underlying the tractability result might be of independent interest

A supersymmetric model for triggering Supernova Ia in isolated white dwarfs

We propose a model for supernovae Ia explosions based on a phase transition to a supersymmetric state which becomes the active trigger for the deflagration starting the explosion in an isolated sub-Chandrasekhar white dwarf star. With two free parameters we fit the rate and several properties of type Ia supernovae and address the gap in the supermassive black hole mass distribution. One parameter is a critical density fit to about $3 \cdot 10^7$ g/cc while the other has the units of a space time volume and is found to be of order $0.05\,$ Gyr $R_E^3$ where $R_E$ is the earth radius. The model involves a phase transition to an exact supersymmetry in a small core of a dense star.Comment: 20 pages, 5 figures, expanded version to be published in Physical Review

Volume 51, Number 2 - February 1971

Volume 51, Number 2 - February 1971. 4 pages including covers and advertisements. McNeil, Paul The Old Streetwalker Richards, Paul J. A LOOK AT VIETNAM IN \u2769 or THE EFFECTS OF SPUTNIK ON AMERICAN EDUCATION McNeil, Paul A LOOK AT INTELLECTUAL SNOBBERY IN \u2771 and/or THE EFFECTS OF AMERICAN EDUCATION ON THE AMERICAN EDUCATED rhys, skyles return of judas viator rhys, skyles spanish soliloquy O\u27Neil, Charles J., Jr. Boston Common rhys, skyles jews, circa 1940 O\u27Neil, Charles J., Jr. How Awesome is this Place Rybarski, Michael A. EXERCISE NO. 3. Gray, Thomas as Mother beams McNeil, Paul CAT\u27S CRADLE Paul, Michael James ROCK AND ROLL THOSE DAYS FOR MIKE MCDONALD Greer, Jim Gousie, Gene Paul, Michael for C. Bucknavage, John Plaintive Recourse rhys, skyles Read Me Charpentier, Robert Your Room O\u27Neil, Charles J., Jr. I, Pygmalion Magner, Tom Tetreault, Philip A. My Life is Living Magner, Tom Drinking thinking they got it mad

HST/NICMOS Imaging of Disks and Envelopes Around Very Young Stars

We present HST/NICMOS observations with 0.1" (15 AU) resolution of six young stellar objects in the Taurus star-formation region. The targets of our survey are three Class I IRAS sources (IRAS 04016+2610, IRAS 04248+2612, and IRAS 04302+2247) and three low-luminosity stars (DG Tau B, Haro 6-5B, and CoKu Tau/1) associated with Herbig Haro jets. The broad-band images show that the near-infrared radiation from these sources is dominated by light scattered from dusty circumstellar material distributed in a region 10 - 15 times the size of our solar system. Although the detailed morphologies of the individual objects are unique, the observed young stellar objects share common features. All of the circumstellar reflection nebulae are crossed by dark lanes from 500 - 900 AU in extent and from less than 50 to 350 AU in apparent thickness. The absorption lanes extend perpendicular to known optical and millimeter outflows in these sources. We interpret the dark lanes as optically thick circumstellar disks seen in silhouette against bright reflection nebulosity. The bipolar reflection nebulae extending perpendicular to the dust lanes appear to be produced by scattering from the upper and lower surfaces of the disks and from dusty material within or on the walls of the outflow cavities. Out of five objects in which the central source is directly detected, two are found to be subarcsecond binaries. This mini-survey is the highest resolution near-infrared study to date of circumstellar environments around solar-type stars with age <= 1 Myr.Comment: 34 pages, 4 figures; also available at http://spider.ipac.caltech.edu/staff/brandner/topics/disks/disks.html ; accepted for publication in AJ (March 1999 issue

Shot Glasses: An American Tradition

My intent in compiling the information contained in this book is for it to be much more than a catalog of shot glasses. It is a history project involving significant effort, for researching this subject has proved to be quite elusive. It is not a topic that has been written about to my knowledge, except when it is mentioned in passing in books about glassware. Even then, rarely more than a page or two are devoted to shot glasses.Master of ArtsLiberal StudiesUniversity of Michigan-Flinthttps://deepblue.lib.umich.edu/bitstream/2027.42/143489/1/Pickvet.pd