Geodesic
A finite graph is the Reeb graph of a Morse circle-valued function
Filomat, Tome 37 (2023) no. 11, p. 3575

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

We show that any non-trivial finite connected graph (allowing loop edges and multiple edges) is isomorphic to the Reeb graph of a Morse circle-valued function on a closed n-manifold of a given dimension n ≥ 2; this manifold roughly resembles a thick version of the graph, we present its construction and study its properties. In the case of surfaces (n = 2), we prove a criterion for when a finite graph can be realized as the Reeb graph of such a function on a given surface.
DOI : 10.2298/FIL2311575G
Classification : 57R35, 58C06, 54C50, 57R30, 05C90
Keywords: Reeb graph, Circle-valued function, Realization problem 
Irina Gelbukh. A finite graph is the Reeb graph of a Morse circle-valued function. Filomat, Tome 37 (2023) no. 11, p. 3575 . doi: 10.2298/FIL2311575G
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     author = {Irina Gelbukh},
     title = {A finite graph is the {Reeb} graph of a {Morse} circle-valued function},
     journal = {Filomat},
     pages = {3575 },
     year = {2023},
     volume = {37},
     number = {11},
     doi = {10.2298/FIL2311575G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2311575G/}
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