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@article{1688903,
author = {Kráľ, Daniel and Lovasz, Laszlo M. and Noel, Jonathan A. and Sosnovec, Jakub},
article_location = {CAMBRIDGE},
article_number = {9},
doi = {http://dx.doi.org/10.19086/da.12058},
keywords = {graph limits; finite forcibility},
language = {eng},
issn = {2397-3129},
journal = {Discrete Analysis},
title = {Finitely Forcible Graphons with an Almost Arbitrary Structure},
url = {http://dx.doi.org/10.19086/da.12058},
volume = {2020},
year = {2020}
}
TY - JOUR
ID - 1688903
AU - Kráľ, Daniel - Lovasz, Laszlo M. - Noel, Jonathan A. - Sosnovec, Jakub
PY - 2020
TI - Finitely Forcible Graphons with an Almost Arbitrary Structure
JF - Discrete Analysis
VL - 2020
IS - 9
SP - 1-36
EP - 1-36
PB - ALLIANCE DIAMOND OPEN ACCESS JOURNALS
SN - 23973129
KW - graph limits
KW - finite forcibility
UR - http://dx.doi.org/10.19086/da.12058
N2 - Graphons are analytic objects representing convergent sequences of large graphs. A graphon is said to be finitely forcible if it is determined by finitely many subgraph densities, i.e., if the asymptotic structure of graphs represented by such a graphon depends only on finitely many density constraints. Such graphons appear in various scenarios, particularly in extremal combinatorics. Lovasz and Szegedy conjectured that all finitely forcible graphons possess a simple structure. This was disproved in a strong sense by Cooper, Kral' and Martins, who showed that any graphon is a subgraphon of a finitely forcible graphon. We strengthen this result by showing for every epsilon > 0 that any graphon spans a 1- epsilon proportion of a finitely forcible graphon.
ER -
KRÁĽ, Daniel, Laszlo M. LOVASZ, Jonathan A. NOEL a Jakub SOSNOVEC. Finitely Forcible Graphons with an Almost Arbitrary Structure. \textit{Discrete Analysis}. CAMBRIDGE: ALLIANCE DIAMOND OPEN ACCESS JOURNALS, 2020, roč.~2020, č.~9, s.~1-36. ISSN~2397-3129. Dostupné z: https://dx.doi.org/10.19086/da.12058.
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