Results 11 to 20 of about 91 (73)
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
(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
wiley +1 more source
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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On correlation of hyperbolic volumes of fullerenes with their properties
Computational and Mathematical Biophysics, 2020 We observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to π /2 in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume.
Egorov A. A., Vesnin A Yu.
doaj +1 more source
On the multiplicative sum Zagreb index of graphs with some given parameters
Journal of Mathematical Inequalities, 2020 The multiplicative sum Zagreb index of a graph G is the product of the sums of degrees of pairs of adjacent vertices. In this work, we obtain the maximum values of the multiplicative sum Zagreb indices with fixed number of cut edges, or cut vertices, or ...
Jianwei Du, Xiaoling Sun
semanticscholar +1 more source
Computing the Hosoya Polynomial of M‐th Level Wheel and Its Subdivision Graph
Journal of Chemistry, Volume 2021, Issue 1, 2021., 2021 The determination of Hosoya polynomial is the latest scheme, and it provides an excellent and superior role in finding the Weiner and hyper‐Wiener index. The application of Weiner index ranges from the introduction of the concept of information theoretic analogues of topological indices to the use as major tool in crystal and polymer studies.
Peng Xu +6 more
wiley +1 more source