On the Connected Blocks Polytope.
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| Title: | On the Connected Blocks Polytope. |
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| Authors: | Bruckamp, Justus1 (AUTHOR) justus.bruckamp@uni-osnabrueck.de, Chimani, Markus1 (AUTHOR) markus.chimani@uni-osnabrueck.de, Juhnke, Martina1 (AUTHOR) martina.juhnke@uni-osnabrueck.de |
| Source: | Discrete & Computational Geometry. Jun2025, Vol. 73 Issue 4, p946-972. 27p. |
| Subjects: | Gröbner bases, Triangulation, Generalization, Eulerian graphs, Polytopes |
| Abstract: | In this paper, we study the connected blocks polytope, which, apart from its own merits, can be seen as the generalization of certain connectivity based or Eulerian subgraph polytopes. We provide a complete facet description of this polytope, characterize its edges and show that it is Hirsch. We also show that connected blocks polytopes admit a regular unimodular triangulation by constructing a squarefree Gröbner basis. In addition, we prove that the polytope is Gorenstein of index 2 and that its h ∗ -vector is unimodal. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | In this paper, we study the connected blocks polytope, which, apart from its own merits, can be seen as the generalization of certain connectivity based or Eulerian subgraph polytopes. We provide a complete facet description of this polytope, characterize its edges and show that it is Hirsch. We also show that connected blocks polytopes admit a regular unimodular triangulation by constructing a squarefree Gröbner basis. In addition, we prove that the polytope is Gorenstein of index 2 and that its h ∗ -vector is unimodal. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 01795376 |
| DOI: | 10.1007/s00454-024-00675-5 |
