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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.