---
res:
bibo_abstract:
- "Hill's Conjecture states that the crossing number cr(\U0001D43E\U0001D45B) of
the complete graph \U0001D43E\U0001D45B in the plane (equivalently, the sphere)
is 14⌊\U0001D45B2⌋⌊\U0001D45B−12⌋⌊\U0001D45B−22⌋⌊\U0001D45B−32⌋=\U0001D45B4/64+\U0001D442(\U0001D45B3)
. Moon proved that the expected number of crossings in a spherical drawing in
which the points are randomly distributed and joined by geodesics is precisely
\ \U0001D45B4/64+\U0001D442(\U0001D45B3) , thus matching asymptotically the conjectured
value of cr(\U0001D43E\U0001D45B) . Let cr\U0001D443(\U0001D43A) denote the
crossing number of a graph \U0001D43A in the projective plane. Recently, Elkies
proved that the expected number of crossings in a naturally defined random projective
plane drawing of \U0001D43E\U0001D45B is (\U0001D45B4/8\U0001D70B2)+\U0001D442(\U0001D45B3)
. In analogy with the relation of Moon's result to Hill's conjecture, Elkies asked
if lim\U0001D45B→∞ cr\U0001D443(\U0001D43E\U0001D45B)/\U0001D45B4=1/8\U0001D70B2
. We construct drawings of \U0001D43E\U0001D45B in the projective plane that
disprove this.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Alan M
foaf_name: Arroyo Guevara, Alan M
foaf_surname: Arroyo Guevara
foaf_workInfoHomepage: http://www.librecat.org/personId=3207FDC6-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Dan
foaf_name: Mcquillan, Dan
foaf_surname: Mcquillan
- foaf_Person:
foaf_givenName: R. Bruce
foaf_name: Richter, R. Bruce
foaf_surname: Richter
- foaf_Person:
foaf_givenName: Gelasio
foaf_name: Salazar, Gelasio
foaf_surname: Salazar
- foaf_Person:
foaf_givenName: Matthew
foaf_name: Sullivan, Matthew
foaf_surname: Sullivan
bibo_doi: 10.1002/jgt.22665
dct_date: 2021^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0364-9024
- http://id.crossref.org/issn/1097-0118
dct_language: eng
dct_publisher: Wiley@
dct_title: Drawings of complete graphs in the projective plane@
...