Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Rowan Rowlands, Sheila Sundaram, Lei Xue
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SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1630-1675, June 2024. Abstract. We define the [math]-cut complex of a graph [math] with vertex set [math] to be the simplicial complex whose facets are the complements of sets of size [math] in [math] inducing disconnected subgraphs of [math]. This generalizes the Alexander dual of a graph complex studied by Fröberg [Topics in Algebra, Part 2, PWN, Warsaw, 1990, pp. 57–70] and Eagon and Reiner [J. Pure Appl. Algebra, 130 (1998), pp. 265–275]. We describe the effect of various graph operations on the cut complex and study its shellability, homotopy type, and homology for various families of graphs, including trees, cycles, complete multipartite graphs, and the prism [math], using techniques from algebraic topology, discrete Morse theory, and equivariant poset topology.
期刊介绍：
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.
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