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pro vyhledávání: '"Bayer, Margaret"'
An outerplanar graph is a planar graph that has a planar drawing with all vertices on the unbounded face. The matching complex of a graph is the simplicial complex whose faces are subsets of disjoint edges of the graph. In this paper we prove that th
Externí odkaz:
http://arxiv.org/abs/2411.04601
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 (20
Externí odkaz:
http://arxiv.org/abs/2407.08158
Autor:
Bayer, Margaret M., Borgwardt, Steffen, Chambers, Teressa, Daugherty, Spencer, Dawkins, Aleyah, Deligeorgaki, Danai, Liao, Hsin-Chieh, McAllister, Tyrrell, Morrison, Angela, Nelson, Garrett, Vindas-Meléndez, Andrés R.
For $\mathbf{b}=(b_1,\dots,b_n)\in \mathbb{Z}_{>0}^n$, a $\mathbf{b}$-parking function is defined to be a sequence $(\beta_1,\dots,\beta_n)$ of positive integers whose nondecreasing rearrangement $\beta'_1\leq \beta'_2\leq \cdots \leq \beta'_n$ satis
Externí odkaz:
http://arxiv.org/abs/2403.07387
A magic labeling of a graph is a labeling of the edges by nonnegative integers such that the label sum over the edges incident to every vertex is the same. This common label sum is known as the index. We count magic labelings by maximum edge label, r
Externí odkaz:
http://arxiv.org/abs/2403.04129
Autor:
Bayer, Margaret, Denker, Mark, Milutinović, Marija Jelić, Rowlands, Rowan, Sundaram, Sheila, Xue, Lei
Publikováno v:
SIAM J. on Discrete Mathematics,Vol. 38 (2), 1630--1675 (2024)
We define the $k$-cut complex of a graph $G$ with vertex set $V(G)$ to be the simplicial complex whose facets are the complements of sets of size $k$ in $V(G)$ inducing disconnected subgraphs of $G$. This generalizes the Alexander dual of a graph com
Externí odkaz:
http://arxiv.org/abs/2304.13675
A (general) polygonal line tiling is a graph formed by a string of cycles, each intersecting the previous at an edge, no three intersecting. In 2022, Matsushita proved the matching complex of a certain type of polygonal line tiling with even cycles i
Externí odkaz:
http://arxiv.org/abs/2211.12559
Autor:
Bayer, Margaret, Denker, Mark, Milutinović, Marija Jelić, Rowlands, Rowan, Sundaram, Sheila, Xue, Lei
Inspired by work of Fr\"oberg (1990), and Eagon and Reiner (1998), we define the \emph{total $k$-cut complex} of a graph $G$ to be the simplicial complex whose facets are the complements of independent sets of size $k$ in $G$. We study the homotopy t
Externí odkaz:
http://arxiv.org/abs/2209.13503
The {\em perfect matching complex} of a graph is the simplicial complex on the edge set of the graph with facets corresponding to perfect matchings of the graph. This paper studies the perfect matching complexes, $\mathcal{M}_p(H_{k \times m\times n}
Externí odkaz:
http://arxiv.org/abs/2209.02803
Autor:
Bayer, Margaret, Goeckner, Bennet, Hong, Su Ji, McAllister, Tyrrell, Olsen, McCabe, Pinckney, Casey, Vega, Julianne, Yip, Martha
Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the c
Externí odkaz:
http://arxiv.org/abs/2005.09628
The matching complex of a graph is the simplicial complex whose vertex set is the set of edges of the graph with a face for each independent set of edges. In this paper we completely characterize the pairs (graph, matching complex) for which the matc
Externí odkaz:
http://arxiv.org/abs/1906.03328