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20 papers · 1 filter
On the -base of Finite Lattices: Semidistributive, Modular, and Geometric Lattices
Kira Adaricheva, Simon Vilmin
Implicational bases are a well-known representation of closure spaces and their closure lattices. This representation is not unique, though, and a closure space usually admits mult…
Separation axiom for geodesic convexity in graphs
Victor Chepoi
Semispaces of a convexity space are maximal convex sets missing a point. The separation axiom asserts that any point and any convex set not containing…
Boundary rigidity of finite CAT(0) cube complexes
Jérémie Chalopin, Victor Chepoi
In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave…
Boundedness for proper conflict-free and odd colorings
Andrea Jiménez, Kolja Knauer, Carla Negri Lintzmayer +7
The proper conflict-free chromatic number, , of a graph is the least such that has a proper -coloring in which for each non-isolated vertex there is a co…
Isometric path complexity of graphs
Dibyayan Chakraborty, Jérémie Chalopin, Florent Foucaud +1
A set of isometric paths of a graph is ``-rooted'', where is a vertex of , if is one of the endpoints of all the isometric paths in . The isometric path co…
ABC(T)-graphs: an axiomatic characterization of the median procedure in graphs with connected and G-connected medians
Laurine Bénéteau, Jérémie Chalopin, Victor Chepoi +1
The median function is a location/consensus function that maps any profile (a finite multiset of vertices) to the set of vertices that minimize the distance sum to vertices fro…