The Average Degree of Minimally Contraction-Critically 5-Connected Graphs
Article first published online: 17 MAY 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 4, pages 331–354, April 2014
How to Cite
Ando, K., Egawa, Y. and Kriesell, M. (2014), The Average Degree of Minimally Contraction-Critically 5-Connected Graphs. J. Graph Theory, 75: 331–354. doi: 10.1002/jgt.21741
- Issue published online: 15 JAN 2014
- Article first published online: 17 MAY 2013
- Manuscript Revised: 12 MAR 2013
- Manuscript Received: 8 MAY 2012
- 5-connected graph;
- contraction-critically 5-connected;
- degree 5 vertex;
- AMS classification;
An edge of a 5-connected graph is said to be 5-removable (resp. 5-contractible) if the removal (resp. the contraction) of the edge results in a 5-connected graph. A 5-connected graph with neither 5-removable edges nor 5-contractible edges is said to be minimally contraction-critically 5-connected. We show the average degree of every minimally contraction-critically 5-connected graph is less than . This bound is sharp in the sense that for any positive real number ε, there is a minimally contraction-critically 5-connected graph whose average degree is greater than .