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If you have any good math exercises to share feel free to contribute them on http://exwiki.org


Dec
7
comment Semi-hamiltonian graph.
@user180834 I wrote a complete solution.
Dec
7
comment Semi-hamiltonian graph.
@user180834 Can you answer the question in the hint?
Dec
7
comment Semi-hamiltonian graph.
What do you mean by semi-Hamiltonian?
Nov
29
comment Diameter of a Connected Graph
@sam_rox Yes, you are right. Thanks for the remark, I've corrected the page.
Nov
20
comment Determinant of the Kronecker product involving the identity
@Surb Err you're right I mean the Kronecker product!
Nov
20
comment orbits/canonical labelling of colored graphs
Hi! I am using Sage which AFAIK does not support this feature.
Nov
11
comment Number of words not having a subword of length k with only one letter
Thanks, that was very useful! Do you perhaps see a way to obtain an asymptotic estimate? I don't see a good way given that the poles of $f(z)$ are not directly known.
Nov
1
comment Determine a formula for the number of triangles in the line graph $L(G)$ in term of quantities in $G$
Just some pointers - every triangle in $G$ is also a triangle in $L(G).$ If $v$ i a vertex of degree $d$ then its edges give rise to $K_{d}$ in $L(G).$
Nov
1
comment Paper claiming a graph isomorphism that isn't actually an isomorphism?
@Zaaier What exactly do you want to implement? Just for isomorphism testing there are many free implementations online.
Oct
28
comment Upper bound for the number of hamilton cycles in a cubic graph
@Peter I forgot to mention that in this context $c$ can as well be infinity.
Oct
27
comment Upper bound for the number of hamilton cycles in a cubic graph
Exactly. What you do know though is that the limit you mention is $\leq c$ for some $c > 0.$
Oct
20
comment Proportion of asymmetric graphs
I believe you can figure this out from the book by Godsil and Royle (algebraic graph theory) see page 24.
Oct
17
comment how should I show that list chromatic number of $K_{3,3}=3$?
Perhaps this helps? exwiki.org/mw/…
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
There you go then!
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
@Peter Yes it is the least example.
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
Hm.. what is surely true is that if $G$ is $2$-edge connected then $L(G)$ is $2$-connected. This may give a clue for counterexamples.
Oct
2
comment $2$-connected graphs with a line graph containing no hamilton cycle
Have you checked this paper sciencedirect.com/science/article/pii/S0893965912001036 dealing with a conjecture of Thomassen, stating that every $4$-connected line graph is hamiltonian? Its not really what you're asking for but it may offer some insight.
Sep
27
comment Length of longest cycle in this graph
I suggest you check the documentation related to the graph theory module sagemath.org/doc/reference/graphs/sage/graphs/graph.html
Sep
27
comment Length of longest cycle in this graph
btw, are you trying to find small planar hypohamiltonian graphs? :)
Sep
27
comment Length of longest cycle in this graph
I am sorry, I meant a .txt file. A simple file that contains the edges in a format that is easy to parse - say dimacs format.