Vertices of Degree 6 for Contraction-critical 6- Connected Graph
QI Deng-ji · Journal of Hubei Institute for Nationalities · 2002
Every contraction-critical 6-connected graph has a vertex of degree 6.Recently,Yuan Xudong proved that every contraction-critical 6-connected graph contains two adjacent vertices of degree 6.In this paper,we proved that there exists a vertex of degree 6 for every vertex of contraction-critical 6-connected graph such that the two vertices are adjacent or the distance of the two vertices is 2. This result gives further discription for vertices of degree 6 in contraction-critical 6- connected graphs.