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Topology of Cut Complexes II
- Publication Year :
- 2024
-
Abstract
- We continue the study of the $k$-cut complex $\Delta_k(G)$ of a graph $G$ initiated in the paper of Bayer, Denker, Jeli\'c Milutinovi\'c, Rowlands, Sundaram and Xue [Topology of cut complexes of graphs, SIAM J. on Discrete Math. 38(2): 1630--1675 (2024)]. We give explicit formulas for the $f$- and $h$-polynomials of the cut complex $\Delta_k(G_1+G_2) $ of the disjoint union of two graphs $G_1$ and $G_2$, and for the homology representation of $\Delta_k(K_m+K_n)$. We also study the cut complex of the squared path and the grid graph. Our techniques include tools from combinatorial topology, discrete Morse theory and equivariant poset topology.<br />Comment: 29 pages, 7 figures, 3 tables
- Subjects :
- Mathematics - Combinatorics
Mathematics - Algebraic Topology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.08158
- Document Type :
- Working Paper