| Naslov: | A note on the 2-colored rectilinear crossing number of random point sets in the unit square |
|---|
| Avtorji: | ID Cabello, Sergio (Avtor)
ID Czabarka, Éva (Avtor)
ID Fabila-Monroy, Ruy (Avtor)
ID Higashikawa, Yuya (Avtor)
ID Seidel, Raimund (Avtor)
ID Székely, László (Avtor)
ID Tkadlec, Josef (Avtor)
ID Wesolek, Alexandra (Avtor) |
|---|
| Datoteke: |  PDF - Predstavitvena datoteka, prenos (504,15 KB)
MD5: B9EB5C7AC15B97E236601B03BBA82579
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s10474-024-01436-9
|
|---|
| Jezik: | Angleški jezik |
|---|
| Tipologija: | 1.01 - Izvirni znanstveni članek |
|---|
| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
|
|---|
| Povzetek: | Let $S$ be a set of four points chosen independently, uniformly at random from a square. Join every pair of points of $S$ with a straight line segment. Color these edges red if they have positive slope and blue, otherwise. We show that the probability that $S$ defines a pair of crossing edges of the same color is equal to $1/4$. This is connected to a recent result of Aichholzer et al. who showed that by $2$-colouring the edges of a geometric graph and counting monochromatic crossings instead of crossings, the number of crossings can be more than halved. Our result shows that for the described random drawings, there is a coloring of the edges such that the number of monochromatic crossings is in expectation ${1 \over 2} - {7 \over 50}$ of the total number of crossings. |
|---|
| Ključne besede: | arrangement of points, flat, hyperplane |
|---|
| Status publikacije: | Objavljeno |
|---|
| Verzija publikacije: | Objavljena publikacija |
|---|
| Datum objave: | 01.06.2024 |
|---|
| Leto izida: | 2024 |
|---|
| Št. strani: | str. 214-226 |
|---|
| Številčenje: | Vol. 173, iss. 1 |
|---|
| PID: | 20.500.12556/DiRROS-20508  |
|---|
| UDK: | 514.17 |
|---|
| ISSN pri članku: | 0236-5294 |
|---|
| DOI: | 10.1007/s10474-024-01436-9 |
|---|
| COBISS.SI-ID: | 206428931 |
|---|
| Opomba: |
|
|---|
| Datum objave v DiRROS: | 03.10.2024 |
|---|
| Število ogledov: | 166 |
|---|
| Število prenosov: | 86 |
|---|
| Metapodatki: |    |
|---|
|
:
|
Kopiraj citat |
|---|
| | | | Objavi na: |  |
|---|
Postavite miškin kazalec na naslov za izpis povzetka. Klik na naslov izpiše
podrobnosti ali sproži prenos. |
