1,145 reputation
813
bio website andrewdouglasking.com
location Vancouver
age 34
visits member for 4 years, 5 months
seen Aug 11 at 20:54
I am interested in graph theory and combinatorial optimization.

Jul
2
awarded  Curious
Mar
12
awarded  Yearling
Feb
6
comment Combinatorial Proof of Weak Perfect Graph Theorem.
Thanks Petr, updated the link.
Feb
6
revised Combinatorial Proof of Weak Perfect Graph Theorem.
updated link
Jan
8
comment How dense is the set of asymmetric graphs?
Is there a simple justification for your first sentence?
Dec
6
comment Expected Value for a Connected Graph
It's easier to think about this in the equivalent model of giving each vertex a uniform random real in $[0,1]$.
Nov
9
awarded  Good Question
Oct
1
answered Does the notion of graphs with vertex multiplicity exist?
Jul
29
comment Hitting all cycles with three disjoint vertex sets
Even any graph containing $K_4$ fails.
Jun
25
awarded  Tumbleweed
May
21
comment Removing edges from Erdős–Rényi graph to make two nodes disconnected
You seem to be saying that if $c = \ln n$, then the maximum degree is going to be at most $2 \ln n / \ln \ln n$. I guess that's not the case?
Apr
6
comment The probability distribution for vertex degree in a unit disc graph generated from random points on a plane
If you use an arbitrarily large plane, or even better, a sphere or torus, shouldn't the degree of a vertex just be Poisson-distributed? I don't really understand the second paragraph, so maybe it could use some clarification. Colourings of random geometric graphs has been studied quite a lot, including by user RJK, who will probably come by in the near future with a more intelligent response.
Apr
5
comment Clique number of a $k$th power of a graph in terms of maximum degree?
Yes; they are related but not equivalent problems, because you could have vertices that are not in your clique, but help to connect vertices. I think the numbers should be close but not equal. (Aside from this question, I have found a better way to solve the problem I was working on.)
Apr
3
revised Clique number of a $k$th power of a graph in terms of maximum degree?
added 151 characters in body
Apr
3
asked Clique number of a $k$th power of a graph in terms of maximum degree?
Mar
29
comment counting k-cliques not also (k+1) on random graphs
Parallel to Brendan's comment, if $k$ is larger than order $\log(n)$, the probability of $\omega(G)$ being $k+1$ is vanishingly small compared to the probability of $\omega(G)$ being $k$. I recommend looking at Chapter 7 of Random Graphs by Janson, Luczak and Rucinski. Note that since you have half the edges, looking at the size of a maximum stable set is equivalent to looking at the size of a maximum clique. You should also look at Section 1.4 if you are unfamiliar with the asymptotic equivalence of $G(n,p)$ and $G(n,m)$.
Mar
24
comment If a graph embeds in the projective plane or the torus is there a bound on the number of edge crossings it has in the plane?
There is another way to read it: What is the smallest function $f$ of $n$ such that any toroidal graph on $n$ vertices can be drawn in the plane with at most $f(n)$ crossings?
Mar
13
comment Disjoint Maximum Independent Sets in $alpha$-critical graphs
I'm pretty sure (*) fails emphatically. As evidence, consider the case in which the edges form a perfect matching. Here $n$ is the maximum stable set still, but since $n>m$ the graph is disconnected. Moreover it fails for $(m,n)=(1,2)$, and I think you should be able to prove that it fails in general using strong induction and observing the new maximum stable set when you remove an edge.
Mar
13
comment Partitioning the vertex set of a graph with a large independent set
In that case, doesn't Colin provide a valid counterexample?
Mar
12
comment regular hyper graph construction
Generating them how? Steiner triple systems are 3-uniform and regular, for an example.