Complete Minors in Cubic Graphs with few short Cycles and Random Cubic Graphs

We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this theorem to show that for any fixed k a random cubic graph contains a Kk-minor asymptotically almost surely.

• Type: Journal
• Year: 2004
• Where: ARSCOM
• Authors: Klas Markstrom
• Keywords: ARSCOM 2004, Cubic Graph, Direct Generalisation, Short Cycles