Realization of a digraph as the Reeb graph of a Morse-Bott function on a given surface

Applications of graph theory (05C90) Critical points and critical submanifolds in differential topology (57R70) Directed graphs (digraphs), tournaments (05C20) Real-valued functions on manifolds (58C05) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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Kronrod-Reeb graphs of functions on noncompact two-dimensional surfaces. I
On representation of the Reeb graph as a sub-complex of manifold
Nonsingular Smale flows on \(S^ 3\)
Singular levels and topological invariants of Morse-Bott foliations on non-orientable surfaces
Kronrod-Reeb graphs of functions on noncompact two-dimensional surfaces. II
Realization of a graph as the Reeb graph of a Morse function on a manifold
Automorphisms of Kronrod-Reeb graphs of Morse functions on compact surfaces
Combinatorial modifications of Reeb graphs and the realization problem
A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function
Criterion for a graph to admit a good orientation in terms of leaf blocks
On Reeb graphs induced from smooth functions on 3-dimensional closed manifolds with finitely many singular values
On handle theory for Morse-Bott critical manifolds
Diffeomorphisms preserving Morse-Bott functions
Morse functions with sphere fibers
Topological classification of simple Morse Bott functions on surfaces
Acyclic Digraphs
Lyapunov Graphs and Flows on Surfaces
Morse-Bott functions with two critical values on a surface
Topological classification of circle-valued simple Morse-Bott functions
Realization of a Graph as the Reeb Graph of a Morse–Bott or a Round Function
Approximation of metric spaces by Reeb graphs: Cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannian manifolds
Reeb Spaces of Smooth Functions on Manifolds
Deformations of functions on surfaces
The co-rank conjecture for 3-manifold groups
Topological classification of circle-valued simple Morse-Bott functions on closed orientable surfaces

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