Matching and Independence Complexes Related to Small Grids
نویسندگان
چکیده
The topology of the matching complex for the 2×n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(∆n ) that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain Ind(∆n ). Furthermore, we determine the Euler characteristic of Ind(∆n ) and prove that several homology groups of Ind(∆n ) are non-zero.
منابع مشابه
un 2 01 6 MATCHING AND INDEPENDENCE COMPLEXES RELATED TO SMALL GRIDS
The topology of the matching complex for the 2 × n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(∆mn ) that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain Ind(∆mn ). Fur...
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عنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017