23 citations · 43 across the 33 of their papers we have counts for
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Extensions of Linear Cycle Sets
Jorge A. Guccione, Juan J. Guccione, Christian Valqui
We generalize the cohomology theory for linear cycle sets introduced by Lebed and Vendramin. Our cohomology classifies extensions of linear cycle sets by trivial ideals, whereas th…
Cocommutative q-cycle coalgebra structures on the dual of the truncated polynomial algebra
Jorge Guccione, Juan José Guccione, Christian Valqui
In order to construct solutions of the braid equation we consider bijective left non-degenerate set-theoretic type solutions, which correspond to regular q-cycle coalgebras. We obt…
Minimal graph in which the intersection of two longest paths is not a separator
Juan Gutiérrez, Christian Valqui
We prove that for a connected simple graph with vertices, and two longest paths and in , the intersection of vertex sets is a separator. Th…
Bi-traceable graphs, the intersection of three longest paths and Hippchen's conjecture
Juan Gutiérrez, Christian Valqui
Let be longest paths in a simple graph. We analyze the possible connections between the components of and introduce the notion of a bi-trac…