Topology of Cut Complexes II

Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/2933

Title:	Topology of Cut Complexes II
Authors:	Bayer, Margaret Denker, Mark Jelić Milutinović, Marija Sundaram, Sheila Xue, Lei
Affiliations:	Topology
Keywords:	disconnected set;graph complex;grid graph;homology representation;homotopy;Morse matching;shellability;squared path graph
Issue Date:	1-Jan-2025
Rank:	M21
Publisher:	Philadelphia : SIAM Publications
Journal:	SIAM Journal on Discrete Mathematics
Abstract:	We continue the study of the k-cut complex Δk(G) of a graph G initiated in the paper of Bayer et al. [SIAM J. Discrete Math., 38 (2024), pp. 1630-1675]. We give explicit formulas for the f- and h-polynomials of the cut complex Δk(G1 + G2) of the disjoint union of two graphs G1 and G2, and for the homology representation of Δk(Km + Kn). 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.
URI:	https://research.matf.bg.ac.rs/handle/123456789/2933
ISSN:	08954801
DOI:	10.1137/24M1676077
Appears in Collections:	Research outputs

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