Projects per year
Abstract
We show that there is a constant c so that for fixed r >= 3 a.a.s. an r-regular graph on n vertices contains a complete graph on c root n vertices as a minor. This confirms a conjecture of Markstrom (Ars Combinatoria 70 (2004) 289-295). Since any minor of an r-regular graph on n vertices has at most m/2 edges, our bound is clearly best possible up to the value of the constant c. As a corollary, we also obtain the likely order of magnitude of the largest complete minor in a random graph G,,,p during the phase transition (i.e., when pn -> 1). (C) 2009 Wiley Periodicals, Inc. Random Struct. Alg., 35, 444-463, 2009
Original language | English |
---|---|
Pages (from-to) | 444-463 |
Number of pages | 20 |
Journal | Random Structures and Algorithms |
Volume | 35 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Dec 2009 |
Keywords
- Hadwiger number
- random regular graphs
- graph minors
Fingerprint
Dive into the research topics of 'Minors in Random Regular Graphs'. Together they form a unique fingerprint.Projects
- 1 Finished
-
Probabilistic Methods in Graph Theory
Kuhn, D. (Principal Investigator) & Osthus, D. (Co-Investigator)
Engineering & Physical Science Research Council
26/04/06 → 25/01/09
Project: Research Councils