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Vertices of degree 6 in a contraction critically 6-connected graph

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

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
378 KB
Volume
273
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

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 (G)| vertices of degree 6.

๐Ÿ“œ SIMILAR VOLUMES

Vertices of degree 6 in a 6-contraction
Vertices of degree 6 in a 6-contraction critical graph
โœ Kiyoshi Ando; Atsushi Kaneko; Ken-ichi Kawarabayashi ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 229 KB

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