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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, +43 authors Bernhard Von Stengel
  • 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)
SUMMARY Cesium-129 is concentrated in the myocardium after intravenous administration permitting my-ocardial imaging. The dosage used was 2-2.5 mCi in dogs and 3-4 mCi in patients. Four or more views with 200,000 counts per view were obtained 30 to 90 minutes after administration. Control images were obtained in 30 dogs. In two dogs anatomic landmarks were(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)