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 $q$.
@article{10_37236_3377,
author = {Felix Lazebnik and Keith E. Mellinger and Oscar Vega},
title = {Embedding cycles in finite planes},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {3},
doi = {10.37236/3377},
zbl = {1295.05134},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3377/}
}
TY - JOUR
AU - Felix Lazebnik
AU - Keith E. Mellinger
AU - Oscar Vega
TI - Embedding cycles in finite planes
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/3377/
DO - 10.37236/3377
ID - 10_37236_3377
ER -
%0 Journal Article
%A Felix Lazebnik
%A Keith E. Mellinger
%A Oscar Vega
%T Embedding cycles in finite planes
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/3377/
%R 10.37236/3377
%F 10_37236_3377
Felix Lazebnik; Keith E. Mellinger; Oscar Vega. Embedding cycles in finite planes. The electronic journal of combinatorics, Tome 20 (2013) no. 3. doi: 10.37236/3377
