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Vertices of Degree 5 in a Contraction Critically 5-connected Graph

โœ Scribed by Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi


Publisher
Springer Japan
Year
2005
Tongue
English
Weight
318 KB
Volume
21
Category
Article
ISSN
0911-0119

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An edge of a 6-connected graph is said to be 6-contractible if the contraction of the edge results in a 6-connected graph. A contraction critically 6-connected graph is a 6-connected graph with no 6-contractible edge. We prove that each contraction critically 6-connected graph G has at least 1 7 |V

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An edge of a \(k\)-connected graph is said to be \(k\)-contractible if the contraction of the edge results in a \(k\)-connected graph. A \(k\)-connected graph with no \(k\)-contractible edge is said to be a \(k\)-contraction critical graph. We prove that every 6 -contraction critical graph of order