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On the Crossing Number of K n without Computer Assistance
Author(s) -
McQuillan Dan,
Richter R. Bruce
Publication year - 2016
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21908
Subject(s) - crossing number (knot theory) , mathematics , class (philosophy) , combinatorics , natural number , discrete mathematics , arithmetic , computer science , artificial intelligence , cartography , geography , intersection (aeronautics)
We present several general results about drawings of K n , as a beginning to trying to determine its crossing number. As application, we give a complete proof that the crossing number of K 9 is 36 and that all drawings in one large, natural class of drawings of K 11 have at least 100 crossings.