VERTICES OF DEGREE 6 IN A CONTRACTION-CRITICAL 6 CONNECTED GRAPH
Min Li · Journal of Guangxi Normal University · 2005
An edge of a 6 connected graph is said to be 6-contractible if its contraction results still in a 6 connected graph.A noncomplete 6 connected graph is called contraction-critical if it has no any 6-contractible edge.Let G be a contraction-critical 6 connected graph.By Egawa's result,G has a vertex of degree 6.Let V_6 denote the set of vertices of degree 6 in G.Recently,Ando et.al showed that there is a constant c such that ｜V_6｜≥c｜V(G)｜,and c≥17.In this note,it is proved that c≥15.