Exact(8)
And we want to end up with an odd length path.
If I take the edge from A to B, I will get to B using an even length path, or an odd length path?
PROFESSOR: So, if I get to A using an even length path, then from there I'll get to B using an odd length path.
We have shown that for two robots, solving it requires the existence of an odd length cycle (Lemma 5).
This invariant, which holds at the beginning of any execution because of the precomputed paths (and ultimately because of the existence of an odd length cycle in G), implies that robots end up at distance exactly one.
A consequence is that the task has a solution for A,B iff for any two vertices of G there is an odd length path, corresponding to a path in (tilde {G}) alternating vertices with id A and B. Notice that the formal specification of the edge covering problem as a triple (langle tilde {I},tilde {G},tilde {Delta }rangle ), depends on the number of robots, and indeed we defined it above for A,B.
Similar(52)
In any case, for every v i and v j, there is a odd length simple path between them.
This was based on a partnership agreement to lead low from any odd length, so West could judge that East held seven spades.
For the case of two robots, edge covering can be solved iff G is connected and contains an odd-length cycle.
Trying to find an odd-length carbon cycle substructure in CID20652954 causes a complexity explosion; for example, matching the cycloheptadecane structure in it takes tens of minutes in all available cartridges before failing.
It is needed the existence of an odd-length path in G from u to v: SO logdiam(G)) is mapped to a path in G from u to v, and each edge of the subdivision is mapped to an edge of the path; however, as explained above, the length of SO logdiam(G)) is odd (more precisely, 3O logdiam(G))), from which follows that the length of the path SO logdiam(G)) is mapped to must be odd.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com