Robert Berke

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We show that the vertices of any plane graph in which every face is of size at least <i>g</i> can be colored by (3g &#192;&#253; 5)=4 colors so that every color appears in every face. This is nearly tight, as there are plane graphs that admit no vertex coloring of this type with more than (3g+1)=4 colors. We further show that the problem of determining(More)
  • Leonard Yves, R Ust, M Sc, Eth In, Eth Bernd Gärtner, Zurich +40 others
  • 2007
The goal of this thesis is to give a better understanding of the linear complementarity problem with a P-matrix (PLCP). Finding a polynomial time algorithm for the PLCP is a longstanding open problem. Such an algorithm would settle the complexity status of many problems reducing to the PLCP. Most of the papers dealing with the PLCP look at it from an(More)
We show that any graph of maximum degree at most ¢ has a two-coloring, such that one color-class is an independent set while the other color induces monochromatic components of order at most £ ¥ ¤ § ¦. On the other hand for any constant¨we exhibit a ©-regular graph, such that the deletion of any independent set leaves at least one component of order greater(More)
This report addresses the problem of identifying a threshold for propagation connectiv-ity in random hypergraphs as specified in [BO09]. In that paper we gave upper and lower bounds for the threshold that left a gap of a factor (log n)(log log n) 2. Unfortunately there is some uncertainty regarding a detail in the lemma that was used to provide the upper(More)
Acknowledgments I would like to thank all the people without whom this thesis would not have been written. In the first place, my thanks go to Emo Welzl for giving me the opportunity to work in his research group and the graduate program Combinatorics, Geometry, and Computation. I would like to express my deep gratitude to my advisor Bernd Gärtner. His(More)
We study relaxations of proper two-colorings, such that the order of the induced monochro-matic components in one (or both) of the color classes is bounded by a constant. A coloring of a graph G is called (C 1 , C 2)-relaxed if every monochromatic component induced by vertices of the first (second) color is of order at most C 1 (C 2 , resp.). We prove that(More)
OBJECTIVE To compare the investigator assessment of patient risk for prescription opioid misuse, abuse, and diversion with patient self-reports of these activities in a population with chronic pain. METHODS As a secondary objective of an open-label, multicenter, primary care-based clinical study to evaluate the success of converting opioid-experienced(More)
OBJECTIVE To evaluate the conversion of opioid-experienced patients with chronic moderate-to-severe pain to extended-release morphine sulfate with sequestered naltrexone hydrochloride (MSN) using a standardized conversion guide. METHODS This open-label, single-arm study was conducted in 157 primary care centers in the United States. A total of 684(More)
Transversals in r-partite graphs with various properties are known to have many applications in graph theory and theoretical computer science. We investigate f-bounded transversals (or f-BT), that is, transversals whose connected components have order at most f. In some sense we search for the the sparsest f-BT-free graphs. We obtain estimates on the(More)