Injective Maps between Flip Graphs
نویسنده
چکیده
We prove that every injective simplicial map F(S) → F(S′) between flip graphs is induced by a subsurface inclusion S → S′, except in finitely many cases. This extends a result of Korkmaz–Papadopoulos which asserts that every automorphism of the flip graph of a surface without boundary is induced by a surface homeomorphism.
منابع مشابه
Counting Edge-Injective Homomorphisms and Matchings on Restricted Graph Classes
We consider the parameterized problem of counting all matchings with exactly k edges in a given input graph G. This problem is #W[1]-hard (Curticapean, ICALP 2013), so it is unlikely to admit f(k) · nO(1) time algorithms. We show that #W[1]-hardness persists even when the input graph G comes from restricted graph classes, such as line graphs and bipartite graphs of arbitrary constant girth and ...
متن کاملDynamics on Networks of Manifolds
We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give ri...
متن کاملExact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism
For graphs G and H , a homomorphism from G to H is a function φ : V (G) → V (H), which maps vertices adjacent in G to adjacent vertices of H . A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H . Many cases of graph homomorphism and locally injective graph homomorphism are NPcomplete, so there is little hope to design polynomial-time...
متن کاملModular dynamical systems on networks
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular ...
متن کاملSimplicial Embeddings between Pants Graphs
We prove that, except in some low-complexity cases, every locally injective simplicial map between pants graphs is induced by a π1-injective embedding between the corresponding surfaces.
متن کامل