---
res:
  bibo_abstract:
  - "Given a set A of n points (vertices) in general position in the plane, the complete
    geometric graph \r\nKn[A] consists of all (n2) segments (edges) between the elements
    of A. It is known that the edge set of every complete geometric graph on n vertices
    can be partitioned into O(n3∕2) crossing-free paths (or matchings). We strengthen
    this result under various additional assumptions on the point set. In particular,
    we prove that for a set A of n randomly selected points, uniformly distributed
    in [0,1]2, with probability tending to 1 as n→∞, the edge set of Kn[A] can be
    covered by O(nlogn) crossing-free paths and by O(n√logn) crossing-free matchings.
    On the other hand, we construct n-element point sets such that covering the edge
    set of Kn[A] requires a quadratic number of monotone paths.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Adrian
      foaf_name: Dumitrescu, Adrian
      foaf_surname: Dumitrescu
  - foaf_Person:
      foaf_givenName: János
      foaf_name: Pach, János
      foaf_surname: Pach
  - foaf_Person:
      foaf_givenName: Morteza
      foaf_name: Saghafian, Morteza
      foaf_surname: Saghafian
      foaf_workInfoHomepage: http://www.librecat.org/personId=f86f7148-b140-11ec-9577-95435b8df824
  - foaf_Person:
      foaf_givenName: Alex
      foaf_name: Scott, Alex
      foaf_surname: Scott
  bibo_doi: 10.2140/cnt.2026.15.73
  bibo_issue: '1'
  bibo_volume: 15
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2996-2196
  - http://id.crossref.org/issn/2996-220X
  dct_language: eng
  dct_publisher: Mathematical Sciences Publishers@
  dct_title: Covering complete geometric graphs by monotone paths@
...