Embedding cycles in finite planes

作者：Lazebnik Felix^*; Mellinger Keith E; Vega Oscar

来源：ELECTRONIC JOURNAL OF COMBINATORICS, 2013, 20(3): P24.

DOI：10.37236/3377

• Graph embeddings
• finite affine plane
• finite projective plane
• cycle
• hamiltonian cycle
• pancyclic graph

We define and study embeddings of cycles infinite affine and projective planes. We show that for all k, 3 %26lt;= k %26lt;= q(2), a k-cycle can be embedded in any affine plane of order q. We also prove a similar result for finite projective planes: for all k, 3 %26lt;= k %26lt;= q(2) + q + 1, a k-cycle can be embedded in any projective plane of order q.

• 出版日期2013-8-23