Andrew D. King
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 Feb 25 comment Meeting management For some reason I can't edit the question, but here goes: There are 60 people. On each of five days, the people are partitioned into ten groups of six for day-long meetings. Is it possible to find a set of five partitions such that no two people meet twice? Feb 25 answered How to find central vertex in a graph? Feb 22 comment Finding local patterns in a circular list Sorry, I meant $O(1)$ time, and $(1-\epsilon)n$ nodes. Feb 22 comment Finding local patterns in a circular list Well, here is a vague set of sufficient conditions: - the pattern always holds somewhere on a circular list - the pattern always holds somewhere on a linear list with property $x$. - given a circular list or a linear list with property $x$, we can find, in $O(\plog n)$ time, a linear sublist with property $x$ containing at most $(1-\epsilon)$ of the nodes. Feb 21 comment A k-1 edge connected k regular graph is matching covered Yes, I just added the missing details. Additionally I originally said "stable set polytope" when I meant to say "perfect matching polytope". Hope this helps. Feb 21 revised A k-1 edge connected k regular graph is matching covered added 1113 characters in body Jan 6 comment Algorithm for calculating the sum-of-squares distance of a rolling window from a given line function So in other words, the line for $y$ is "glued to" the window, and you move the window along the $x$-axis? Jan 6 comment Algorithm for calculating the sum-of-squares distance of a rolling window from a given line function Can you use $\Theta(n)$ storage? Why not just make a queue of squares of differences. When you advance the window by 1, simply add the new square difference and subtract the square distance that disappears from the window. This is constant time per step once you spend $O(n)$ time setting up the initial window. Or do you mean that the window is moved to some position arbitrarily far away? Dec 9 comment Characteristics of locally triangle-free graph This is a comment instead of an answer since I omit so many details. It's fairly easy to see that $G$ can be any tree. Fix a root and lay out the tree in such a way that the angle between any two children of a vertex is very small. If you do this with increasingly small angles as you move away from the root, you can complete the triangulation using points on an arc very far away from the tree, so that the tree is at the centre of the circle containing the arc. I believe it should be straightforward to modify the construction so that $G$ can actually be any acyclic graph. Nov 21 comment SWAT vs Rioters (cops vs robbers variant) If it is no, then see what happens for chordal graphs, then graphs of bounded treewidth. Nov 21 comment SWAT vs Rioters (cops vs robbers variant) Just a few thoughts. First, it is probably best, at least to start, to insist that $S$ and $R$ are increasing functions. It seems like the graph should be SWAT-win if SWAT can eradicate the rioters given any initial configuration. Characterizing SWAT-win graphs in a very general way seems very difficult, so I would start with the obvious first steps: Trees, cycles, outerplanar graphs. Then a first question becomes: Given a weighted graph and initial numbers of SWAT/Rioters, can we determine if it is SWAT-win in polynomial time? I suspect the answer is no, but I'm not sure. Nov 8 comment probability distribution of hitting nodes on a finite graph random walk Also sometimes known as small world graphs. Oct 24 answered A k-1 edge connected k regular graph is matching covered Oct 18 comment Has anyone seen this graph? In particular this graph is the smallest simple cubic graph with no perfect matching. Oct 17 comment What is this subclass of $k$-colorable graphs called? I would call such a graph edge-maximal $k$-colourable. This property can be useful in induction on the number of non-edges in a graph. Aug 31 awarded Necromancer Jul 27 comment Can you prove that hypergraphs with n-1 edges are partially 2 colorable? Good! I was a little worried that Hall's theorem was the theorem you wanted to avoid. Jul 27 answered Can you prove that hypergraphs with n-1 edges are partially 2 colorable? Jul 7 awarded Critic Jun 15 comment Fast removal of weighted edges in a graph in a way such that all shortest paths are preserved So is this equivalent to computing all-pairs shortest path, then deleting all edges not contained in some shortest path? And I don't really understand the question... use the Floyd-Warshall algorithm if you want it to be simple, and use this Sudakov result you mention if you want it to be fast. I highly doubt that you would easily be able to construct the edge set faster than that, but I may be wrong.