Complete solutions to the Oberwolfach problem for an infinite set of orders |
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| Authors: | Darryn Bryant Victor Scharaschkin |
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| Institution: | aThe University of Queensland, Department of Mathematics, Qld 4072, Australia |
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| Abstract: | Let n 3 and let F be a 2-regular graph of order n. The Oberwolfach problem OP(F) asks for a 2-factorisation of Kn if n is odd, or of Kn−I if n is even, in which each 2-factor is isomorphic to F. We show that there is an infinite set  of primes congruent to  such that OP(F) has a solution for any 2-regular graph F of order  . We also show that for each of the infinitely many  with  prime, OP(F) has a solution for any 2-regular graph F of order n. |
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| Keywords: | Oberwolfach problem 2-factorisations Graph decompositions Graph factorisations |
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