Treatment of terminal phosphide anion [PNb(N[Np]Ar)3] ([Na(OEt2)] + salt, Ar 1⁄4 3,5-Me2C6H3) with two diphenylketene equivalents led to isolation of anion [P(C{CPh2}O)2Nb(N[Np]Ar)3] in 78% yield as its [Na(THF)] salt. The latter reacts with diphenylketene (1 equiv) to provide the triple diphenylketene addition product [P(C{CPh2}O)3Nb(N[Np]Ar)3] in 88% yield as its [Na(THF)] salt; the same mate...

Let Mk ⊆ N be a given set that consists of k noncontiguous integers. Define Exact-Mk-Colorability to be the problem of determining whether χ(G), the chromatic number of a given graph G, equals one of the k elements of the set Mk exactly. In 1987, Wagner [Wag87] proved that Exact-Mk-Colorability is BH2k(NP)-complete, where Mk = {6k + 1, 6k + 3, . . . , 8k − 1} and BH2k(NP) is the 2kth level of t...

In the Minimum Sum Edge Coloring problem we have to assign positive integers to the edges of a graph such that adjacent edges receive different integers and the sum of the assigned numbers is minimal. We show that the problem is (a) NP-hard for planar bipartite graphs with maximum degree 3, (b) NP-hard for 3-regular planar graphs, (c) NP-hard for partial 2-trees, and (d) APX-hard for bipartite ...

The page-number of a directed acyclic graph (a DAG, for short) is the minimum k which DAG has topological order and k-coloring its edges such that no two same color cross, i.e., have alternating endpoints along order. In 1999, Heath Pemmaraju conjectured recognition DAGs with 2 NP-complete proved recognizing 6 [SIAM J. Computing, 1999]. Binucci et al. recently strengthened this result by provin...

We show that the Min Cut Linear Arrangement Problem (Min Cut) is NP-complete for trees with polynomial size edge weights and derive from this the NP-completeness of Min Cut for planar graphs with maximum vertex degree 3. This is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/ White Pebble Demand, and Topological Bandwidth for planar graphs with maximum v...

We have evaluated 4 radioiodinated mouse monoclonal anticarcinoembryonic antigen antibodies (MAbs) by using the GW-39 human colorectal tumor xenograft transplanted i.m. in immunocompetent hamsters to determine whether there were any differences in their tumor localization properties. Additional comparisons were made to affinity-purified goat anticarcinoembryonic antigen antibody. Statistically ...

In this lecture, we first examine several classes of NP-hardness and polynomial time algorithms which arise from differences in how integers are encoded in problem input. We then look at the 3-partition problem, which is very useful for proving the strongest notion of NP-hardness. Finally, we use reduction from 3-partition to prove NP-hardness for a handful of problems, including a set of 4 pac...

In computational geometry, packing problems ask whether a set of rigid pieces can be placed inside a target region such that no two pieces overlap. The triangle packing problem is a packing problem that involves triangular pieces, and it is crucial for algorithm design in many areas, including origami design, cutting industries, and warehousing. Previous works in packing algorithms have conject...