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On the local profiles of trees. (English) Zbl 1330.05037

Summary: We study the local profiles of trees. We show that in contrast with the situation for general graphs, the limit set of \(k\)-profiles of trees is convex. We initiate a study of the defining inequalities of this convex set. Many challenging problems remain open.

MSC:

05C05 Trees
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References:

[1] Hatami, Undecidability of linear inequalities in graph homomorphism densities, J Am Math Soc 24 (2) pp 547– (2011) · Zbl 1259.05088 · doi:10.1090/S0894-0347-2010-00687-X
[2] Huang, On the 3-local profiles of graphs, arXiv preprint, arXiv (2012)
[3] Razborov, Flag algebras, J Symbol Logic pp 1239– (2007) · Zbl 1146.03013 · doi:10.2178/jsl/1203350785
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