---
res:
  bibo_abstract:
  - "Motivated by the successful application of geometry to proving the Harary--Hill
    conjecture for “pseudolinear” drawings of $K_n$, we introduce “pseudospherical”
    drawings of graphs. A spherical drawing of a graph $G$ is a drawing in the unit
    sphere $\\mathbb{S}^2$ in which the vertices of $G$ are represented as points---no
    three on a great circle---and the edges of $G$ are shortest-arcs in $\\mathbb{S}^2$
    connecting pairs of vertices. Such a drawing has three properties: (1) every edge
    $e$ is contained in a simple closed curve $\\gamma_e$ such that the only vertices
    in $\\gamma_e$ are the ends of $e$; (2) if $e\\ne f$, then $\\gamma_e\\cap\\gamma_f$
    has precisely two crossings; and (3) if $e\\ne f$, then $e$ intersects $\\gamma_f$
    at most once, in either a crossing or an end of $e$. We use properties (1)--(3)
    to define a pseudospherical drawing of $G$. Our main result is that for the complete
    graph, properties (1)--(3) are equivalent to the same three properties but with
    “precisely two crossings” in (2) replaced by “at most two crossings.” The proof
    requires a result in the geometric transversal theory of arrangements of pseudocircles.
    This is proved using the surprising result that the absence of special arcs (coherent
    spirals) in an arrangement of simple closed curves characterizes the fact that
    any two curves in the arrangement have at most two crossings. Our studies provide
    the necessary ideas for exhibiting a drawing of $K_{10}$ that has no extension
    to an arrangement of pseudocircles and a drawing of $K_9$ that does extend to
    an arrangement of pseudocircles, but no such extension has all pairs of pseudocircles
    crossing twice.\r\n@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
    orcid: 0000-0003-2401-8670
  - foaf_Person:
      foaf_givenName: R. Bruce
      foaf_name: Richter, R. Bruce
      foaf_surname: Richter
  - foaf_Person:
      foaf_givenName: Matthew
      foaf_name: Sunohara, Matthew
      foaf_surname: Sunohara
  bibo_doi: 10.1137/20M1313234
  bibo_issue: '2'
  bibo_volume: 35
  dct_date: 2021^xs_gYear
  dct_identifier:
  - UT:000674142200022
  dct_isPartOf:
  - http://id.crossref.org/issn/0895-4801
  dct_language: eng
  dct_publisher: Society for Industrial and Applied Mathematics@
  dct_title: Extending drawings of complete graphs into arrangements of pseudocircles@
...