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$\begingroup$ What philosophical reasons? $\endgroup$

Gil Kalai
– Gil Kalai

2010-12-14 21:45:13 +00:00
Commented Dec 14, 2010 at 21:45
7

$\begingroup$ I would say the Erdős–Renyi/Rado graph en.wikipedia.org/wiki/Rado_graph rather than this, if you're looking for something from graph theory. This occurs as the Fraïssé limit of the category of finite graphs and embeddings golem.ph.utexas.edu/category/2009/11/fraisse_limits.html $\endgroup$

David Roberts
– David Roberts ♦

2010-12-14 23:57:48 +00:00
Commented Dec 14, 2010 at 23:57
$\begingroup$ David: isn't that graph also known as "the" random graph on a countably infinite vertex set? $\endgroup$

Yemon Choi
– Yemon Choi

2010-12-15 00:16:27 +00:00
Commented Dec 15, 2010 at 0:16
$\begingroup$ Gil: For the reason that it can easily demonstrate the existence of a graph with a beautiful and intricate structure without explicitly exhibiting it. Although you could argue that we may as well say that a coin flip is is an intricate and beautiful structure. Also, it should maybe be disqualified by your "single object" specification. $\endgroup$

Andrew D. King
– Andrew D. King

2010-12-15 03:27:03 +00:00
Commented Dec 15, 2010 at 3:27

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