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May
7
comment Looking for algorithms capable of modifying graph structure
@Will You can most likely make a quick Sage function to do what you want
Apr
13
comment Subgroups of the dihedral group D_n modulo Aut(D_n)
@DerekHolt Derek, thanks that helped. If you're willing to copy paste your comment into an answer I'll upvote& accept it.
Apr
13
comment Edge and vertex connectivity of bipartite graph
Do you see that every vertex of this graph has precisely $n-1$ neighbors? How many vertex/edge disjoint paths are between two vertices in $X$. What about a pair of vertices $x \in X,y \in Y$
Apr
13
comment Edge and vertex connectivity of bipartite graph
The graph you describe is the disjoint union of $n$ edges. Hence if $n > 1$ the graph is not connected. But as I said I think you're confused with the definition and in fact want to consider $K_{n,n}$-matching.
Apr
13
comment Edge and vertex connectivity of bipartite graph
So in this case your graph is a matching which is a disconnected graph for $n > 1.$
Apr
13
comment Edge and vertex connectivity of bipartite graph
Are you sure you don't mean that every vertex has precisely $n-1$ neighbours? That would give you $K_{n,n}$ minus one matching.
Apr
7
comment Subgroups of the dihedral group D_n modulo Aut(D_n)
@DerekHolt Hm.. Why is there no fusion for $n$ odd and why is it enough to consider the automorphism $r \mapsto r$ and $s \mapsto rs$?
Mar
31
comment All non-isomorphic transitive actions of the Dihedral group
@DerekHolt Could you please elaborate a bit more about this? I spent a day on it but don't see an easy way to deduce that for $n$ odd we only need consider subgroups up to conjugacy and the structure of the isomorphism classes under $\rm{Aut}(G)$. Thanks
Mar
30
comment All non-isomorphic transitive actions of the Dihedral group
@LeeMosher Which theorem exactly? I only covered Lemma1.6B which allows one to find transitive actions up to equivalence.
Mar
30
comment All non-isomorphic transitive actions of the Dihedral group
@LeeMosher Yes, but I don't know how this gives me all actions of $D_n$ modulo isomorphism
Mar
25
comment Outer automorphism of $S_6$ and conjugate stabilizers
Could you please clarify why $g((1,2))$ commutes with every element of the stabilizer of $1$ and $2$? Why does it follow that $g$ is the identity map? Is it because it fixes all the transpositions?
Mar
6
comment Bounding probability of some events with bounded depdendence
@Math1000 The complement of the event $A_1.$
Feb
26
comment Probabilistic method: vertex disjoint cycles in digraphs
@ManuelLafond Interesting. Where did you find this proof? I think one can fix it by using the asymmetric LLL perhaps at the expense of a worse constant.
Feb
26
comment Probabilistic method: vertex disjoint cycles in digraphs
@ManuelLafond I've spoken with the author and he confirmed its a mistake. One would somehow have to include this event C as well.
Feb
19
comment Does there exists a $k$-critical graph having connectivity $2$ for every $k\geq 3$?
Note that by definition, $K_k$ is $2$-connected for any $k > 2.$
Feb
18
comment For every r exists large enough n such that any graph…
Which propositions are you allowed to use then?
Feb
17
comment Finding the spanning subgraphs of a complete bipartite graph
@chowching I suggest that for a start you look at Harary's and Palmer's book called "graphical enumeration"
Feb
17
comment Finding the spanning subgraphs of a complete bipartite graph
@chowching You can but the formula will most likely require using computer computations.
Feb
17
comment Finding the spanning subgraphs of a complete bipartite graph
@chowching You should be more specific about what you're looking for. Note that in general there is no closed formula for the number of bipartite graphs with bipartitions of cardinality n and m.
Feb
17
comment min degree at least $n+1/2$, every edge on Hamilton cycle
I guess you must visualize this thing. Just to be sure $G/e$ denotes the graph obtained by contracting the edge $e$?