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We call the natural number $n$ a partition number $\iff$ $$ \exists d | n: \gcd\left(d,\frac{n}{d}\right)=1 \text{ and } \Omega(d) = \Omega\left(\frac{n}{d}\right)\;, $$ where $\Omega$ counts the ...

The Max-3-DCC is the variant of vertex cycle cover problem where each of the vertex disjoint oriented cycles consists of at least 3 arcs and every vertex belongs to exactly one of those cycles; ...

[I posted this on Math Stack Exchange about two weeks ago, but didn't get any reply, so I'm trying it here.] Consider the following simplified form of "Gerrymandering": You have $n^2$ ...

This question is motivated by my impression, that finding better heuristics for the TSP problem (or any other $NP$-complete problem) is "only" of practical interest, but doesn't provide any progress ...

For a given $n \times m$ matrix A with $m>>n$ and a given vector $\vec b \in \mathbb{F}^{n \times 1}$, and given that $A\vec{x}=\vec{b}$ for at least one $\vec{x} \in \mathbb{F}^{m \times 1}$, ...

From the observation, that a bipartite graph doesn't contain odd cycles, it would seem natural to attempt to destroy all odd cycles in the most efficient way, by either removing edges or vertices of ...