TY - JOUR
T1 - Topological graphs with no large grids
AU - Pach, János
AU - Pinchasi, Rom
AU - Sharir, Micha
AU - Tóth, Géza
PY - 2005/9
Y1 - 2005/9
N2 - Let G be a topological graph with n vertices, i.e., a graph drawn in the plane with edges drawn as simple Jordan curves. It is shown that, for any constants k,l, there exists another constant C(k,l), such that if G has at least C(k,l)n edges, then it contains a k×l-gridlike configuration, that is, it contains k+l edges such that each of the first k edges crosses each of the last l edges. Moreover, one can require the first k edges to be incident to the same vertex.
AB - Let G be a topological graph with n vertices, i.e., a graph drawn in the plane with edges drawn as simple Jordan curves. It is shown that, for any constants k,l, there exists another constant C(k,l), such that if G has at least C(k,l)n edges, then it contains a k×l-gridlike configuration, that is, it contains k+l edges such that each of the first k edges crosses each of the last l edges. Moreover, one can require the first k edges to be incident to the same vertex.
KW - Crossing edges
KW - Topological graphs
UR - http://www.scopus.com/inward/record.url?scp=27544442925&partnerID=8YFLogxK
U2 - 10.1007/s00373-005-0616-1
DO - 10.1007/s00373-005-0616-1
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AN - SCOPUS:27544442925
SN - 0911-0119
VL - 21
SP - 355
EP - 364
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 3
ER -