Geodesic
Cycle construction and geodesic cycles with application to the hypercube
Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 27-43.

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Construction of cycles in a graph is investigated, where cycles from particular subsets (such as bases) are added together so that each partial sum is also a cycle or each new cycle intersects the sum of the preceding terms in a nontrivial path. Starting with the geodesic cycles, a hierarchical construction is given. For the hypercube graph, geodesic cycles are characterized, and it is shown how hypercube geodesic cycles can be constructed in two steps from a special basis. Applications are given to inferring commutativity of a diagram in a groupoid from commutativity of some of its cycles.
DOI : 10.26493/1855-3974.450.0b6
Keywords: Robust cycle basis, forced commutativity of groupoid diagram, Cayley graph 
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Paul C. Kainen. Cycle construction and geodesic cycles with application to the hypercube. Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 27-43. doi : 10.26493/1855-3974.450.0b6. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.450.0b6/

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