Abstract
In 1962 Pósa conjectured that every graph G on n vertices with minimum degree contains the square of a hamiltonian cycle. In 1996 Fan and Kierstead proved the path version of Pósa's Conjecture. They also proved that it would suffice to show that G contains the square of a cycle of length greater than. Still in 1996, Komlós, Sárközy, and Szemerédi proved Pósa's Conjecture, using the Regularity and Blow-up Lemmas, for graphs of order n ≥ n0, where n0 is a very large constant. Here we show without using these lemmas that n0:= 2 × 108 is sufficient. We are motivated by the recent work of Levitt, Sárközy and Szemerédi, but our methods are based on techniques that were available in the 90's.
Original language | English (US) |
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Pages (from-to) | 507-525 |
Number of pages | 19 |
Journal | Random Structures and Algorithms |
Volume | 39 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2011 |
Keywords
- Powers of cycles
- Pósa's Conjecture
- Square cycle
ASJC Scopus subject areas
- Software
- General Mathematics
- Computer Graphics and Computer-Aided Design
- Applied Mathematics