Results 31 to 40 of about 2,863,059 (142)
Signed Projective Cubes, a Homomorphism Point of View
Journal of Graph Theory, Volume 113, Issue 1, Page 38-56, September 2026.ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen +2 more
wiley +1 more source
On the chromatic number of q-Kneser graphs [PDF]
, 2011 We show that the q-Kneser graph $qK_{2k:k}$ (the graph on the k-subspaces of a 2k-space over GF(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number $q^k + q^{k-1}$ for k = 3 and for k
A. E. Brouwer +8 more
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Sensitivity and Hamming Graphs
Journal of Graph Theory, Volume 112, Issue 3, Page 296-305, July 2026.ABSTRACT For any m ≥ 3 we show that the Hamming graph H ( n , m ) admits an imbalanced partition into m sets, each inducing a subgraph of low maximum degree. This improves previous results by Tandya and by Potechin and Tsang, and disproves the Strong m‐ary Sensitivity Conjecture of Asensio, García‐Marco, and Knauer.
Sara Asensio +3 more
wiley +1 more source
On the Euler characteristic of S$S$‐arithmetic groups
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We show that the sign of the Euler characteristic of an S$S$‐arithmetic subgroup of a simple algebraic group depends on the S$S$‐congruence completion only, except possibly in type 6D4${}^6 D_4$. Consequently, the sign is a profinite invariant for such S$S$‐arithmetic groups with the congruence subgroup property. This generalizes previous work
Holger Kammeyer, Giada Serafini
wiley +1 more source
Stability of reverse isoperimetric inequalities in the plane: Area, Cheeger, and inradius
Bulletin of the London Mathematical Society, Volume 58, Issue 2, February 2026.Abstract In this paper, we present stability results for various reverse isoperimetric problems in R2$\mathbb {R}^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for λ$\lambda$‐convex bodies — convex bodies with the property that each of their boundary points p$p$ supports a ball of radius 1/λ$1/\lambda$ so that the ...
Kostiantyn Drach, Kateryna Tatarko
wiley +1 more source
A full classification of the isometries of the class of ball‐bodies
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3691-3698, December 2025.Abstract Complementing our previous results, we give a classification of all isometries (not necessarily surjective) of the metric space consisting of ball‐bodies, endowed with the Hausdorff metric. ‘Ball‐bodies’ are convex bodies which are intersections of translates of the Euclidean unit ball.
Shiri Artstein‐Avidan +2 more
wiley +1 more source
The Chromatic Number of Kneser Hypergraphs via Consensus Division [PDF]
We show that the Consensus Division theorem implies lower bounds on the chromatic number of Kneser hypergraphs, offering a novel proof for a result of Alon, Frankl, and Lovász (Trans. Amer. Math. Soc., 1986) and for its generalization by Kř\\u27ıž (Trans.
Haviv, Ishay
core +2 more sources
Normal covering numbers for Sn$S_n$ and An$A_n$ and additive combinatorics
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3307-3325, November 2025.Abstract The normal covering number γ(G)$\gamma (G)$ of a noncyclic group G$G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for γ(Sn)$\gamma (S_n)$ and γ(An)$\gamma (A_n)$ depending on the arithmetic structure of n$n$. In particular we determine the limsups over γ(Sn)/n$\gamma (S_n) / n$ and γ(An)
Sean Eberhard, Connor Mellon
wiley +1 more source
On Kneser solutions of the $n$-th order nonlinear differential inclusions [PDF]
, 2019 summary:The paper deals with the existence of a Kneser solution of the $n$-th order nonlinear differential inclusion \begin {eqnarray} {x}^{(n)}(t)\in -A_{1}(t,x(t),\ldots ,x^{(n-1)}(t)){x}^{(n-1)}(t)-\ldots -A_{n}(t,x(t),\ldots ,&x^{(n-1)}(t))x(t ...
Pavlačková, Martina
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Asymmetric graphs with quantum symmetry
Proceedings of the London Mathematical Society, Volume 131, Issue 5, November 2025.Abstract We present an infinite sequence of finite graphs with trivial automorphism group and non‐trivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are the first examples of any asymmetric classical space that has non‐trivial quantum symmetries.
Josse van Dobben de Bruyn +2 more
wiley +1 more source