A bowtie is a graph on an even number of vertices, say 2g, in which there are 2 disjoint cliques of size g with exactly one edge between the 2 cliques. Consider the Bowtie problem: Input: an undirected graph G=(V,E) and a nonnegative integer g. Output: two disjoint sets of vertices S and T such that their union is a bowtie of size 2g, if such graph exists. This is, S must be a clique on g vertices, T must be a clique in g vertices and exactly one edge connects the two sets.  Show that the Bowtie problem is NP-complete.

All problems in the class NP can be solved by some algorithm in exponential time.

The liver is the largest internal organ that has many metabolic functions and well over 300 total functions.  Which of these is not a function of the liver? 

We saw in class how to reduce SAT to 3-SAT by transforming each clause of a boolean function into new clauses with at most three literals. If we apply such transformation to the clause:

A type of muscle contraction in which the muscle does not shorten, but its tension increases is called  

Calculate ΔG°rxn for the reaction below. ClO(g) + O3(g) → Cl(g) + 2 O2(g) Use the following reactions with known ΔG°rxn values 2 O3(g) → 3 O2(g); ΔG°rxn = +489.6 kJ Cl(g) + O3(g) → ClO(g) + O2(g); ΔG°rxn = -34.5 kJ

Select the Fair Use factor that best describes the scenario. While commenting on the movie, The Sixth Sense, Steven described how shocked he was to learn that Bruce Willis’ character had been dead all along.

In which way does a U.S. Intellectual Property artifact enter the Public Domain?

Consider the Clique-3 problem: Input: an undirected graph G=(V,E) such that every vertex has degree at most three. Output: a subgraph of G that is a clique of maximal size.  Check all true statements:

The spinal cord and the brain make up the Central Nervous System.