Justin
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 May7 answered Is there a standard way to compute $\lim\limits_{n\to\infty}(\frac{n!}{n^n})^{1/n}$? Apr18 comment Non-disjoint partition of a graph into cliques of bounded size Reading the context you added - if you just want to make sure the graph is connected, computing the connected components of a graph is quite easy. From there it is a simple matter of adding edges between the components. I'm not sure how the "sets" you've described work (where do new edges go?), but there are a number of metrics which are easy to compute which may assist you in determining edges to add. Edge-connectivity, min-cuts, diameter of a graph, and max distance from a vertex to any other vertex are all useful and can be ways to measure "connectivity". Apr17 answered Finding a point above the line in $O(\log n)$ Apr16 awarded Supporter Apr15 comment Non-disjoint partition of a graph into cliques of bounded size Degree-based clique growing could be an interesting attempt. Start by computing the degree of each node (note that each node has a set of neighbors [edges]). Start with your highest degree node. Pick the neighbor with highest degree and intersect the neighbor sets [denote this set $S$]. Pick the node $n$ from $S$ with highest degree and intersect the neighbors of $n$ with $S$ and rename that $S$. Repeat. Once $S$ is empty, pick a new node by taking the highest degree node that is not yet in a clique and repeat. This has lots of flaws, but it's hard to optimize without a precise goal. Apr15 answered Non-disjoint partition of a graph into cliques of bounded size Apr15 answered How important is programming for mathematicians? Apr15 answered Help in Independence of events Apr13 awarded Teacher Apr13 answered Probability axiomatic definition problem Apr12 awarded Analytical