Embedding 5-cycle systems into pentagon triple systems |
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| Authors: | Elizabeth J Billington CC Lindner |
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| Institution: | a Centre for Discrete Mathematics and Computing, Department of Mathematics, The University of Queensland, QLD 4072, Australia
b Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849-5307, USA |
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| Abstract: | We show that the spectrum for pentagon triple systems is the set of all n≡1,15,21 or  . We then construct a 5-cycle system of order 10n+1 which can be embedded in a pentagon triple system of order 30n+1 and also construct a 5-cycle system of order 10n+5 which can be embedded in a pentagon triple system of order 30n+15, with the possible exception of embedding a 5-cycle system of order 21 in a pentagon triple system of order 61. |
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| Keywords: | Cycle system Embedding Pentagon triple system |
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