Contractible Edges in 7-Connected Graphs |
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Authors: | Su Jian ji Yuan Xudong |
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Institution: | (1) Department of Mathematics, Guangxi Normal University, 541004 Guilin, P.R.China |
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Abstract: | An edge of a k-connected graph is said to be a k-contractible edge, if its contraction yields again a k-connected graph. A noncomplete k-connected graph possessing no k-contractible edges is called contraction critical k-connected. Recently, Kriesell proved that every contraction critical 7-connected graph has two distinct vertices of degree
7. And he guessed that there are two vertices of degree 7 at distance one or two. In this paper, we give a proof to his conjecture.
The work partially supported by NNSF of China(Grant number: 10171022) |
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