Results 11 to 20 of about 971 (113)
Correlations in totally symmetric self‐complementary plane partitions
Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 493-526, December 2021., 2021 Abstract Totally symmetric self‐complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well‐known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in 1/12 of a hexagon with free boundary to express them as perfect matchings of a family of non‐bipartite planar graphs ...
Arvind Ayyer, Sunil Chhita
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Coloring the Voronoi tessellation of lattices
Journal of the London Mathematical Society, Volume 104, Issue 3, Page 1135-1171, October 2021., 2021 Abstract In this paper we define the chromatic number of a lattice: It is the least number of colors one needs to color the interiors of the cells of the Voronoi tessellation of a lattice so that no two cells sharing a facet are of the same color. We compute the chromatic number of the root lattices, their duals, and of the Leech lattice, we consider ...
Mathieu Dutour Sikirić +3 more
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Deforming cubulations of hyperbolic groups
Journal of Topology, Volume 14, Issue 3, Page 877-912, September 2021., 2021 Abstract We describe a procedure to deform cubulations of hyperbolic groups by ‘bending hyperplanes’. Our construction is inspired by related constructions like Thurston's Mickey Mouse example, walls in fibred hyperbolic 3‐manifolds and free‐by‐Z groups, and Hsu–Wise turns.
Elia Fioravanti, Mark Hagen
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A new obstruction for normal spanning trees
Bulletin of the London Mathematical Society, Volume 53, Issue 4, Page 1220-1227, August 2021., 2021 Abstract In a paper from 2001 (Journal of the LMS), Diestel and Leader offered a proof that a connected graph has a normal spanning tree if and only if it has no minor obtained canonically from either an (ℵ0,ℵ1)‐regular bipartite graph or an order‐theoretic Aronszajn tree. In particular, this refuted an earlier conjecture of Halin's that only the first
Max Pitz
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Sparse Kneser graphs are Hamiltonian
Journal of the London Mathematical Society, Volume 103, Issue 4, Page 1253-1275, June 2021., 2021 Abstract For integers k⩾1 and n⩾2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k‐element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs.
Torsten Mütze +2 more
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(Un)distorted stabilisers in the handlebody group
Journal of Topology, Volume 14, Issue 2, Page 460-487, June 2021., 2021 Abstract We study geometric properties of stabilisers in the handlebody group. We find that stabilisers of meridians are undistorted, while stabilisers of primitive curves or annuli are exponentially distorted for large enough genus.
Sebastian Hensel
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Quasi‐isometric diversity of marked groups
Journal of Topology, Volume 14, Issue 2, Page 488-503, June 2021., 2021 Abstract We use basic tools of descriptive set theory to prove that a closed set S of marked groups has 2ℵ0 quasi‐isometry classes, provided that every non‐empty open subset of S contains at least two non‐quasi‐isometric groups. It follows that every perfect set of marked groups having a dense subset of finitely presented groups contains 2ℵ0 quasi ...
A. Minasyan, D. Osin, S. Witzel
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The extremal number of longer subdivisions
Bulletin of the London Mathematical Society, Volume 53, Issue 1, Page 108-118, February 2021., 2021 Abstract For a multigraph F, the k‐subdivision of F is the graph obtained by replacing the edges of F with pairwise internally vertex‐disjoint paths of length k+1. Conlon and Lee conjectured that if k is even, then the (k−1)‐subdivision of any multigraph has extremal number O(n1+1k), and moreover, that for any simple graph F there exists ε>0 such that ...
Oliver Janzer
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Computational complexity of network vulnerability analysis
Acta Universitatis Sapientiae: Informatica, 2022 Residual closeness is recently proposed as a vulnerability measure to characterize the stability of complex networks. Residual closeness is essential in the analysis of complex networks, but costly to compute.
Berberler Murat Erşen
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Graph theoretic and algorithmic aspect of the equitable coloring problem in block graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs.
Hanna Furmańczyk, Vahan Mkrtchyan
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