A new degree sum condition for the existence of a contractible edge in a κ-connected graph

Kriesell has proved that every noncomplete κ-connected (κ≠7) graph has a κ-contractible edge (i.e., an edge whose contraction yields again a κ-connected graph), if the degree sum of any two vertices with distance at most two is at least . And he guessed that the degree sum condition can be relaxed for only adjacent pairs. In this paper, we verified that is true for κ⩾8.