Related papers: Graph-theoretic conditions for injectivity of func…
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
In the enriched setting, the notions of injective and projective model structures on a category of enriched diagrams also make sense. In this paper, we prove the existence of these model structures on enriched diagram categories under local…
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…
We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…
The theory of graph limits is only understood to any nontrivial degree in the cases of dense graphs and of bounded degree graphs. There is, however, a lot of interest in the intermediate cases. It appears that the most important…
Let $G$ be a connected graph and $\mathcal{P}(G)$ a graph parameter. We say that $\mathcal{P}(G)$ is feasible if $\mathcal{P}(G)$ satisfies the following properties: (I) $\mathcal{P}(G)\leq \mathcal{P}(G_{uv})$, if $G_{uv}=G[u\to v]$ for…
We consider the problem of the observability of positively expansive maps by the time series associated to continuous real functions. For this purpose we prove a general result on the generic observability of a locally injective map of a…
We consider non-singular and Jacobian maps whose components are polynomial in the variable y. We prove that if a map has y-degree one, then it is the composition of a triangular map and a quasi-triangular map. We also prove that…
A graphon satisfies the $H$-property if graphs sampled from it contain a Hamiltonian decomposition almost surely, which in turn implies that the corresponding network topologies are, e.g., structurally stable and structurally ensemble…
We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. Only…
Two criteria for planarity of a Feynman diagram upon its propagators (momentum flows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while…
Definable continuous injective maps defined on definable open sets into the Euclidean spaces of the same dimension are open maps in definably complete locally o-minimal expansions of ordered groups.
Given a closed, convex and pointed cone K in R^n, we present a result which infers K-irreducibility of sets of K-quasipositive matrices from strong connectedness of certain bipartite digraphs. The matrix-sets are defined via products, and…
We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, strengthening an analogous result in the random setting by…
In this paper we propose a spectral flow for graph Laplacians, and prove that it counts the number of nodal domains for a given Laplace eigenvector. This extends work done for Laplacians on $\mathbb{R}^n$ to the graph setting. We mention…
Some conditions for the Galois map to be injective are given in the groupoid acting on a noncommutative ring context. In the particular case in which the Galois extension is a central Galois algebra, it is given a complete characterization…
We derive sufficient conditions for exact functors on locally finite abelian categories to preserve Loewy diagrams of objects. We apply our results to determine sufficient conditions for induction functors associated to simple current…