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Results tagged with graph-reconstruction
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user 9025
Questions related to graph reconstruction, the problem of reconstructing a graph from a set or deck (multiset) of subgraphs.
7
votes
Accepted
Reconstructing the number of Hamiltonian cycles
Bill Kocay found a more direct combinatorial method to reconstruct the number of hamiltonian cycles and some other spanning subgraphs. It is in his paper "Some new methods in reconstruction theory", …
- 37.7k
5
votes
Reconstructing graphs with vertices of degree $k$ and $k-1$
Not many people work on the classical reconstruction conjecture these days, probably because only very difficult subproblems remain. The only recent good result I am aware of is this one by Brignall, …
- 37.7k
4
votes
Less general edge reconstruction problem for simple graphs
Except for finitely many cases, $G$ can be reconstructed from the largest of $E^-(G)$ and $E^+(G)$. Note that you have the edge-decks of both $G$ and its complement.
Lovász proved that $G$ is edge-re …
- 37.7k
0
votes
edge graph reconstruction conjecture : set vs multi set
The two problems you mention are not the same, though it is obvious that one implies the other. Nobody knows if they are equivalent. Probably the reason that the "set" version is less known is that it …
- 37.7k