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]]>The fact that the labelling of the edges is so important to this problem has always confused me, especially as I intuitively do not think of the neighbors of a vertex being as an ordered set.

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]]>Label the vertices of an n vertex unit disk graph so that adjacency can be determined by the labels alone, where the metric is to minimise the largest label size of the family (adjacency labeling scheme for unit disk graphs in the literature).

I have nothing better than the one for general graphs (label size n/2+4 explicit, n/2-1 possible).

In the other direction- show a lower bound, again, I have nothing better than log n +O(1).

The same situation occurs in segment intersection graphs.

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]]>More than that, creating such a concentration of wonderful people is a recipe for making great advances, and I am looking forward to the enjoying the research fruits of the Stanford theory group, as well as visiting there (and reminiscing with Greg about the good old days ðŸ™‚ ).

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