Embedding Cycles in Finite Planes

Felix Lazebnik, Keith E. Mellinger, Oscar Vega


We define and study embeddings of cycles in finite affine and projective planes. We show that for all $k$, $3\le k\le q^2$,  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 $k$, $3\le k\le q^2+q+1$,  a $k$-cycle can be embedded in any projective plane of order $q$.


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

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