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

Authors:
Su Jianji;Yuan Xudong
Affiliations:
Department of Mathematics, Guangxi Normal University, 541004, Guilin, PR China;Department of Mathematics, Guangxi Normal University, 541004, Guilin, PR China
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

Citing 3
Cited 0

Generalizations of critical connectivity of graphs

Discrete Mathematics - First Japan Conference on Graph Theory and Applications
A degree sum condition for the existence of a contractible in a k-connected graph

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications

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Abstract

Kriesell has proved that every noncomplete @k-connected (@k7) graph has a @k-contractible edge (i.e., an edge whose contraction yields again a @k-connected graph), if the degree sum of any two vertices with distance at most two is at least 2@?5@k4@?-1. And he guessed that the degree sum condition can be relaxed for only adjacent pairs. In this paper, we verified that is true for @k=8.