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Characterizing Graphs with Crossing Number at Least 2
Author(s) -
Arroyo Alan,
Richter R. Bruce
Publication year - 2017
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.22102
Subject(s) - combinatorics , crossing number (knot theory) , mathematics , vertex (graph theory) , disjoint sets , graph , discrete mathematics , intersection (aeronautics) , engineering , aerospace engineering
Our main result includes the following, slightly surprising, fact: a 4‐connected nonplanar graph G has crossing number at least 2 if and only if, for every pair { e , f } of edges having no common incident vertex, there are vertex‐disjoint cycles in G with one containing e and the other containing f .
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