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Contractible Triples in Highly Connected Graphs

✍ Scribed by Shinya Fujita; Ken-ichi Kawarabayashi


Book ID
105764864
Publisher
Springer
Year
2010
Tongue
English
Weight
231 KB
Volume
14
Category
Article
ISSN
0218-0006

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## Abstract For a graph __G__ we define a graph __T__(__G__) whose vertices are the triangles in __G__ and two vertices of __T__(__G__) are adjacent if their corresponding triangles in __G__ share an edge. Kawarabayashi showed that if __G__ is a __k__‐connected graph and __T__(__G__) contains no ed

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A subgraph H of a 3-connected finite graph G is called contractible if H is connected and G&V(H) is 2-connected. This work is concerned with a conjecture of McCuaig and Ota which states that for any given k there exists an f (k) such that any 3-connected graph on at least f (k) vertices possesses a