Timeline for Infinite graphs with number of common neighbors given for each pair of vertices
Current License: CC BY-SA 3.0
4 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 12, 2016 at 6:33 | comment | added | Dominic van der Zypen | Thanks for your comment - could you post it as an answer so we can close this thread? | |
| Apr 11, 2016 at 14:01 | comment | added | YCor | Assume we have 2 distinct elements $W,X$ such that $c(\{W,X\})=2$, $c(\{U,V\})\le 1$ for all other pairs. Let $P,Q$ be the elements in $N(W)\cap N(X)$. So $WPZQ$ forms a square (with 4 distinct vertices, but possibly extra edges, i.e. possibly not a full subgraph). In particular, $W,X$ are distinct elements in $N(P)\cap N(Q)$, hence $c(\{P,Q))\ge 2$. This forces $\{P,Q\}=\{W,X\}$, contradiction. So such a function $c$ cannot be realized. | |
| Apr 11, 2016 at 12:57 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |