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1d
comment Can a graph be reconstructed from its cycle lengths?
If two $2$-connected graphs have the same number of blobs of every size, and if they have the same number of vertices (edges), must they have the same number of edges (vertices)?
1d
comment Can a graph be reconstructed from its cycle lengths?
Oh right, I forgot $2$-connected. Are the questions about reconstruction (a) the number of vertices and (b) the number of edges two independent questions, or are they equivalent, or is one easier than the other?
1d
comment Can a graph be reconstructed from its cycle lengths?
I believe you are asking, in other words, if two graphs have the same number of Hamiltonian induced subgraphs of order $n$ for each $n$, does it follow that they have (a) the same number of vertices and (b) the same number of edges? Have I got it right?
2d
comment Infinite graphs isomorphic to their line graph
A connected graph of cardinality $\aleph_\omega$ does not necessarily have a vertex of degree $\aleph_\omega$.
2d
comment Is it possible to create an infinite sequence in which no subsequence is repeated 3 times in a row?
The Kolakoski sequence is another example.
Jan
22
awarded  Necromancer
Jan
22
comment Consequences of ZF+“all subsets of reals are Lebesgue measurable”
For the title it looks like you're asking about consequences of "all sets of reals are Lebesgue measurable". But from the body of the question is sounds more like you're asking about consequences of "there is a total $\sigma$-additive (but not necessarily translation-invariant?) extension of Lebesgue measure. Which is it? For the latter, you don't have to drop the axiom of choice, it could happen in ZFC.
Jan
21
answered Infimum of partitions
Jan
16
comment How did Ramanujan discover this identity?
@ZurabSilagadze Yes, that's the obvious answer to how Ramanujan got the identities. But how did the Goddess of Namagiri discover them?
Jan
9
comment Minimality condition in a certain class of hypergraphs
What is the difference in meaning between "$(V,E)$ is a flag complex" and "$E$ is the family of all independent sets for some graph on the vertex set $V$"? What am I missing?
Jan
5
comment Theorem versus Proposition
It is a matter of taste.
Jan
5
comment Theorem versus Proposition
Is there a reason why an author would want or need to tell his readers which results he is proud of and which he is not proud of? Or why a reader would want to know that?
Jan
5
comment Theorem versus Proposition
Labeling some results as 'propositions' meaning 'trivial theorems' is inappropriate because it smacks of snobbery and false humility. The reader can judge for himself whether the result is trivial, and his opinion may differ from the author's.
Jan
5
answered Theorem versus Proposition
Jan
5
comment Theorem versus Proposition
A great mathematician once told me that theorems should be called 'theorems' and calling them 'propositions' is a kind of snobbery.
Dec
22
comment Anti-compactness
Does the term "anti-compact" in this sense have a history or did you just invent it? It has been used for spaces in which every compact set is finite; see Paul Bankston, The total negation of a topological property, Illinois J. Math. 23 (1979), 241-252.
Dec
22
comment For any two noncrossing partitions $p, q$ of $n$, is the graph of geodesics from $p$ to $q$ in $NC(n)$ connected?
What is a noncrossing partition of a number $n$? You don't mean partitions of the set $[n]=\{1,2,\dots,n\}$?
Dec
18
comment Rooks in three dimensions
I am confused. In the first sentence, you say it's still open whether or not any finite number of rooks can force checkmate. In the second sentence, you say that 96 rooks can force checkmate. I suspect that it's the first sentence which I am parsing incorrectly, but in that case I have no idea what it is supposed to mean.
Dec
17
comment finding dominating cycles in $2K_2$-free graphs
Where, by the "complement" of a cycle $C$ in a graph $G$, you really mean the graph $G-V(C)$. Did I guess right?
Dec
13
revised Strongest large cardinal axiom compatible with $V = L$?
Corrected a word in the quotation.