Academic Journal
Enumeration of Intersection Graphs of x-Monotone Curves
| Τίτλος: | Enumeration of Intersection Graphs of x-Monotone Curves |
|---|---|
| Συγγραφείς: | Fox, Jacob, Pach, János, Suk, Andrew |
| Συνεισφορές: | Jacob Fox and János Pach and Andrew Suk |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Έτος έκδοσης: | 2024 |
| Συλλογή: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Θεματικοί όροι: | Enumeration, intersection graphs, pseudo-segments, x-monotone |
| Περιγραφή: | A curve in the plane is x-monotone if every vertical line intersects it at most once. A family of curves are called pseudo-segments if every pair of them have at most one point in common. We construct 2^Ω(n^{4/3}) families, each consisting of n labelled x-monotone pseudo-segments such that their intersection graphs are different. On the other hand, we show that the number of such intersection graphs is at most 2^O(n^{3/2-ε}), where ε > 0 is a suitable constant. Our proof uses an upper bound on the number of set systems of size m on a ground set of size n, with VC-dimension at most d. Much better upper bounds are obtained if we only count bipartite intersection graphs, or, in general, intersection graphs with bounded chromatic number. |
| Τύπος εγγράφου: | article in journal/newspaper conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | Is Part Of LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.4 |
| DOI: | 10.4230/LIPIcs.GD.2024.4 |
| Διαθεσιμότητα: | https://doi.org/10.4230/LIPIcs.GD.2024.4 https://nbn-resolving.org/urn:nbn:de:0030-drops-212887 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.4 |
| Rights: | https://creativecommons.org/licenses/by/4.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.6498074D |
| Βάση Δεδομένων: | BASE |
| DOI: | 10.4230/LIPIcs.GD.2024.4 |
|---|