Generic algorithms for some decision problems on fasciagraphs and rotagraphs

A fasciagraph consists of a sequence of copies of the same graph, each copy being linked to the next one according to a regular scheme. More precisely, a fasciagraph is characterized by an integer n (the number of copies or fibers) and a mixed graph M . In a rotagraph, the last copy is also linked to the first one. In the literature, similar methods were used to address various problems on rotagraphs and fasciagraphs. The goal of our work is to define a class of decision problems for which this kind of method works. For this purpose, we introduce the notion of pseudo- d -local q -properties of fasciagraphs and rotagraphs. For a mixed graph M and a pseudo- d -local q -property P , we propose a generic algorithm for rotagraphs (respectively, fasciagraphs) that computes in one run the data that allow one to decide, for any integer n ≥ d (respectively, n ≥ d + 2 ), whether the rotagraph (respectively, fasciagraph) of length n based on M satisfies P , using only a small number of elementary operations independent of n .