A square-cycle is the graph obtained from a cycle by joining every pair of vertices of distance two in the cycle. The length of a square-cycle is the number of vertices in it. Let G be a graph on n vertices with minimum degree at least 2/3n and let c be the maximum length of a square-cycle in G. Pósa and Seymour conjectured that c = n. In this paper, it is proved that either c = n or 1/2n ≤ c ≤ 2/3n. As an application of this result, it is shown that G has two vertex-disjoint square-cycles C1 and C2 such that V(G) = V(C1) ∪ V(C2).
|Original language||English (US)|
|Number of pages||16|
|Journal||Journal of Graph Theory|
|State||Published - Nov 1996|
ASJC Scopus subject areas
- Geometry and Topology