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The crossing number of K 11 is 100
Author(s) -
Pan Shengjun,
Richter R. Bruce
Publication year - 2007
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.20249
Subject(s) - crossing number (knot theory) , combinatorics , mathematics , simple (philosophy) , graph , exploit , graph theory , discrete mathematics , computer science , philosophy , intersection (aeronautics) , computer security , epistemology , engineering , aerospace engineering
The crossing number of K n is known for n ⩽ 10. We develop several simple counting properties that we shall exploit in showing by computer that cr ( K 11 = 100, which implies that cr ( K 12 ) = 150. We also determine the numbers of non‐isomorphic optimal drawings of K 9 and K 10 . © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 128–134, 2007