DNA fragmentation is a critical component of apoptosis but it has not been characterized in nonapoptotic forms of cell death, such as necrosis and autophagic cell death. In mammalian apoptosis, caspase-activated DNase cleaves DNA into nucleosomal fragments in dying cells, and subsequently DNase II, an acid nuclease, completes the DNA degradation but acts… (More)
The Frieze-Kannan regularity lemma is a powerful tool in combinatorics. It has also found applications in the design of approximation algorithms and recently in the design of fast combinatorial algorithms for boolean matrix multiplication. The algorithmic applications of this lemma require one to efficiently construct a partition satisfying the conditions… (More)
In 1966, Gallai asked whether every connected graph has a vertex that is common to all its longest paths. The answer to this question is negative. We prove that the answer is positive for outerplanar graphs. Another related question was raised in 1995 at the British Combinatorial Conference: Do any three longest paths in a connected graph have a vertex in… (More)
If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.
NOTICE This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information,… (More)
We study a combinatorial game called Bichromatic Triangle Game, defined as follows. Two players R and B construct a triangulation on a given planar point set V. Starting from no edges, they take turns drawing one straight edge that connects two points in V and does not cross any of the previously drawn edges. Player R uses color red and player B uses color… (More)