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Jul
19
comment Graph Theory:Folkman Graph
A good start would be to give a definition/construction of Folkman's graph that will allow to describe its automorphism group. Unless you are happy with a proof involving Sage math :)
Jul
13
comment A construction of a Hadamard matrix
@darijgrinberg Thank you - that helped. I'd be glad to accept this as an answer in case you want to copy paste the comments as an answer.
Jun
19
comment Graphs with 12 edges over the vertices $\{1,2,…,12\}$ have two vertices with a degree of 5
First of all, are you counting up to isomorphism of graphs or are the graphs labelled?
Jun
2
comment Where to learn Combinatorics & Graph Theory further?
Perhaps you may find useful this (modest) list of exercises from graph theory exwiki.org/mw/index.php?title=Graph_theory
May
30
comment number of cycles in arbitrary graph
Hint. If you add an edge to a spanning tree you obtain a cycle. Adding distinct edges gives you distinct cycles.
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 $k > 2.$