Graphs being locally isomorphic but not isomorphic (2) #4990
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* theorems moved from mathboxes to main: ~elrab2w, ~elab2gw, ~elabgw, ~3rspcedvdw, ~fimarab * new theorems in main: ~rexlimdvvva, ~f1ocoima * new auxiliary theoems in AV's mathbox: ~3f1oss1, ~3f1oss2 * new theorems for closed neighborhoods in AV's mathbox: ~predgclnbgrel, ~clnbgredg, ~clnbgrssedg * typo detected by GL fixed in section header "Triangles in graphs" * new theorems for triangles in AV's mathbox: ~grtrimap * new theorems for local isomorphisms between grahs in AV's mathbox: ~uspgrlim (and lemmas), ~usgrlimprop, ~grlimgrtri
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Since this PR is mainly about my mathbox (and 3 theorems moved from mathboxes to main and 2 new simple theorems in main), I will merge this PR on Monday latest, unless there are any objections until then. |
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Unfortunately, the example which I have chosen does not work. The two graphs are also not locally isomorphic, see theorem ~usgrexmpl12ngrlic in this PR! The graphs consisting of 6 vertices and 7 edges are too small, I thing 8 vertices and 9 edges are required (the example graphs in MathOverflow have 10 vertices and 11 edges. The brute force methods I used to prove the corresponding theorems will not be feasible anymore for such graphs, so more general concepts (cycles of 4 edges, unions of graphs, k-stars, etc.) must be studied. I think we have to put issue #4808 on hold now...
Details of this PR:
HandGare not locally isomorphic: ~usgrexmpl12ngrlic