Results 61 to 70 of about 238 (165)
Surface subgroups for cocompact lattices of isometries of H2n$\mathbb {H}^{2n}$
Journal of Topology, Volume 19, Issue 3, September 2026.Abstract We prove the existence of surface subgroups within any cocompact lattice Γ$\Gamma$ in SO(2n,1)$\mathrm{SO}(2n,1)$ for n⩾2$n\geqslant 2$. This result addresses the cases missing from the work of Hamenstädt in 2015, who constructed surface subgroups in cocompact lattices for all other rank‐1 simple Lie groups of noncompact type.
Jeremy Kahn, Zhenghao Rao
wiley +1 more source
On Oriented Colourings of Graphs on Surfaces
Journal of Graph Theory, Volume 112, Issue 4, Page 357-369, August 2026.ABSTRACT For an oriented graph G, the least number of colours required to oriented colour G is called the oriented chromatic number of G and denoted χ o ( G ). For a non‐negative integer g let χ o ( g ) be the least integer such that χ o ( G ) ≤ χ o ( g ) for every oriented graph G with Euler genus at most g.
Alexander Clow
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Asymmetric Results About Graph Homomorphisms
Random Structures &Algorithms, Volume 69, Issue 1, August 2026.ABSTRACT Many important results in extremal graph theory can be roughly summarized as “if a triangle‐free graph G$$ G $$ has certain properties, then it has a homomorphism to a triangle‐free graph Γ$$ \Gamma $$ of bounded size.” For example, bounds on homomorphism thresholds give such a statement if G$$ G $$ has sufficiently high minimum degree, and ...
Lior Gishboliner +2 more
wiley +1 more source
Groups with a finite Busemann boundary are virtually cyclic
Bulletin of the London Mathematical Society, Volume 58, Issue 8, August 2026.Abstract This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric‐functional boundary. We show that if there exists a Cayley graph with finitely many Busemann points, then the underlying group is virtually cyclic.
Corentin Bodart +2 more
wiley +1 more source
List Homomorphisms to Reflexive Graphs
Journal of Combinatorial Theory, Series B, 1998 Let \(H\) be a fixed graph. In analogy to list colouring problems, we introduce the following list homomorphism problem: Given an input graph \(G\) and for each vertex \(v\) of \(G\) a `list' \(L(v) \subseteq V(H)\), decide whether or not there is a homomorphism (edge-preserving mapping of vertices) \(f : G \to H\) such that \(f(v) \in L(v)\) for each \
Tomás Feder, Pavol Hell
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A birational description of the minimal exponent
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We give a description of the minimal exponent of a hypersurface using higher direct images of suitably twisted sheaves of log forms on a log resolution.
Qianyu Chen, Mircea Mustaţă
wiley +1 more source
Graph Homomorphisms for Quantum Players
, 2012 A homomorphism from a graph X to a graph Y is an adjacency preserving mapping f:V(X) -> V(Y). We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph X admits a homomorphism to Y. This is a generalization of the well-studied graph coloring game.
Mančinska, Laura, Roberson, David
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Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract In 1973, Erdős conjectured the existence of high girth (n,3,2)$(n,3,2)$‐Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate version of Erdős' conjecture. Recently, Kwan, Sah, Sawhney, and Simkin proved Erdős' conjecture.
Michelle Delcourt, Luke Postle
wiley +1 more source
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract How hard is it to program n$n$ robots to move about a long narrow aisle while making a series of r−2$r-2$ intermediate stops, provided only w$w$ of the robots can fit across the width of the aisle? In this paper, we answer this question by calculating the rth$r{\text{th}}$‐sequential topological complexity of conf(n,w)$\text{conf}(n,w)$, the ...
Nicholas Wawrykow
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On Random Graph Homomorphisms into Z
Journal of Combinatorial Theory, Series B, 2000 AbstractGiven a bipartite connected finite graph G=(V, E) and a vertex v0∈V, we consider a uniform probability measure on the set of graph homomorphisms f:V→Z satisfying f(v0)=0. This measure can be viewed as a G-indexed random walk on Z, generalizing both the usual time-indexed random walk and tree-indexed random walk. Several general inequalities for
Itai Benjamini +2 more
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