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math.CO2023
Discrete Algebraic sets in Discrete Manifolds
Oliver Knill
A discrete d-manifold is a finite simple graph G=(V,E) where all unit spheres are (d-1)-spheres. A d-sphere is a d-manifold for which one can remove a vertex to make it contractibl…
math.CO2023
Arboricity and Acyclic Chromatic Number
Oliver Knill
A theorem of Hakimi, Mitchem and Schmeichel from 1996 states that the edge arboricity arb(G) of a graph is bounded above by the acyclic chromatic number acy(G). We can improve this…
math.GT2023
On the arboricity of manifolds
Oliver Knill
The arboricity of a discrete 2-sphere is always 3. The arboricity of any other discrete 2-dimensional surface is always 4. For d-manifolds of dimension larger than 2, the arboricit…