Embedding Cycles in Finite Planes

Felix Lazebnik, Keith E. Mellinger, Oscar Vega

Abstract


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 $q$.

Keywords


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

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