| Tartalom: |
http://real.mtak.hu/186620/ |
| Archívum: |
REAL |
| Gyűjtemény: |
Status = Published
Type = Article
Subject = Q Science / természettudomány: QA Mathematics / matematika: QA166-QA166.245 Graphs theory / gráfelmélet
|
| Cím: |
A Full Characterization of Invariant Embeddability of Unimodular Planar Graphs
|
| Létrehozó: |
Timár, Ádám
Tóth, László Márton
|
| Kiadó: |
John Wiley & Sons, Inc.
|
| Dátum: |
2024
|
| Téma: |
QA166-QA166.245 Graphs theory / gráfelmélet
|
| Tartalmi leírás: |
When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry‐invariant? This question was answered for one‐ended unimodular graphs in Benjamini and Timar, using the fact that such graphs automatically have locally finite (simply connected) drawings into the plane. For the case of graphs with multiple ends the question was left open. We revisit Halin's graph theoretic characterization of graphs that have a locally finite embedding into the plane. Then we prove that such unimodular random graphs do have a locally finite invariant embedding into the Euclidean or the hyperbolic plane, depending on whether the graph is amenable or not.
|
| Nyelv: |
angol
|
| Típus: |
Article
NonPeerReviewed
info:eu-repo/semantics/article
|
| Formátum: |
text
|
| Azonosító: |
Timár, Ádám and Tóth, László Márton (2024) A Full Characterization of Invariant Embeddability of Unimodular Planar Graphs. RANDOM STRUCTURES & ALGORITHMS, 64 (2). pp. 320-353. ISSN 1042-9832 (print); 1098-2418 (online)
|
| Kapcsolat: |
MTMT:34199970 DOI: 10.1002/rsa.21188
|
