On derivatives of graphon parameters

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• 作者：Lá ; szló ; Mikló ; s Lová ; sz^a ; ^{lmlovasz@math.mit.edu" class="auth_mail" title="E-mail the corresponding author} ; Yufei Zhao^b ; ¹ ; ^{yufei.zhao@maths.ox.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Graphons ; Graph limits ; Graph homomorphisms ; Gâ ; teaux derivatives
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：145
• 期：Complete
• 页码：364-368
• 全文大小：243 K

文摘

We give a short elementary proof of the main theorem in the paper “Differential calculus on graphon space” by Diao et al. (2015) [2], which says that any graphon parameters whose (N+1)$(N+1)$-th derivatives all vanish must be a linear combination of homomorphism densities t(H,−)$t(H,-)$ over graphs H on at most N edges.