Graph Products and New Solutions to Oberwolfach Problems

Gloria Rinaldi, Tommaso Traetta

Abstract


We introduce the circle product, a method to construct simple graphs starting from known ones. The circle product can be applied in many different situations and when applied to regular graphs and to their decompositions, a new regular graph is obtained together with a new decomposition. In this paper we show how it can be used to construct infinitely many new solutions to the Oberwolfach problem, in both the classic and the equipartite case.


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