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Edges and Kuratowski Subgraphs of Non‐Planar Graphs
Author(s) -
Širáň Jozef
Publication year - 1983
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19831130118
Subject(s) - mathematics , subdivision , combinatorics , planar graph , planar , graph , outerplanar graph , polyhedral graph , planar straight line graph , 1 planar graph , discrete mathematics , pathwidth , chordal graph , line graph , geography , computer science , computer graphics (images) , archaeology
It is proved that any edge of a 4‐connected non‐planar graph G of order at least 6 lies in a subdivision of K 3,3 in G. For any 3‐connected non‐planar graph G of order at least 6 we show that G contains at most four edges which belong to no subdivisions of K 3,3 in G .
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