• Corpus ID: 212633706

Generalized chessboard complexes and discrete Morse theory

@article{Jojic2020GeneralizedCC,
  title={Generalized chessboard complexes and discrete Morse theory},
  author={Duvsko Joji'c and Gaiane Panina and Sinivsa T. Vre'cica and Rade T. vZivaljevi'c},
  journal={arXiv: Metric Geometry},
  year={2020}
}
Chessboard complexes and their generalizations, as objects, and Discrete Morse theory, as a tool, are presented as a unifying theme linking different areas of geometry, topology, algebra and combinatorics. Edmonds and Fulkerson bottleneck (minmax) theorem is proved and interpreted as a result about a critical point of a discrete Morse function on the Bier sphere of an associated simplicial complex $K$. We illustrate the use of "standard discrete Morse functions" on generalized chessboard… 
2 Citations

Figures from this paper

A multiset extension of the optimal colored Tverberg theorem
The type A colored Tverberg theorem of Blagojevic, Matschke, and Ziegler provides optimal bounds for the colored Tverberg problem, under the condition that the number of intersecting rainbow
The coloured Tverberg theorem, extensions and new results
We prove a multiple coloured Tverberg theorem and a balanced coloured Tverberg theorem, applying different methods, tools and ideas. The proof of the first theorem uses a multiple chessboard complex

References

SHOWING 1-10 OF 57 REFERENCES
Multiple chessboard complexes and the colored Tverberg problem
Chessboard complexes indomitable
On discrete Morse functions and combinatorial decompositions
On the Betti Numbers of Chessboard Complexes
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This
Topology of matching, chessboard, and general bounded degree graph complexes
Abstract.We survey results and techniques in the topological study of simplicial complexes of (di-, multi-, hyper-)graphs whose node degrees are bounded from above. These complexes have arisen in a
Decompositions and Connectivity of Matching and Chessboard Complexes
Abstract New lower bounds for the connectivity degree of the r-hypergraph matching and chessboard complexes are established by showing that certain skeleta of such complexes are vertex
Shellability of chessboard complexes
AbstractThe matchings in a complete bipartite graph form a simplicial complex, which in many cases has strong structural properties. We use an equivalent description aschessboard complexes: the
Torsion in the matching complex and chessboard complex
Symmetric multiple chessboard complexes and a new theorem of Tverberg type
AbstractWe prove a new theorem of Tverberg–van Kampen–Flores type, which confirms a conjecture of Blagojević et al. about the existence of ‘balanced Tverberg partitions’ (Conjecture 6.6 in [Tverberg
...
...