6

What you look for in question Q1 is known as an $f$-factor of the graph. Here $f$ is a non-negative integer valued function on the vertices, $f(v)$ specifying the degree we want in the subgraph at vertex $v$. Q2 is looking for a so called $(g,f)$ factor, where $g(v)$ is a lower bound and $f(v)$ is an upper bound on the degree of the sought subgraph at each ...


2

I like to introduce Vertex-Cover as a problem in which the underlying graph models a museum, so that the vertices represent the museum rooms and the edges represent the corridors. Then, it is easy for the students to understand that minimising the number of guards required to watch over the museum corresponds to finding a vertex cover. The guards are placed ...


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