Motivated by structural decompositions and other asymptotic properties of graphs we define the notions in the title and show the wide spectrum of examples of nowhere dense graphs. This has several algorithmic consequences and it generalizes and improves earlier results.

Given an oriented graph G, the modular flow polynomial φG(k) counts the number of nowhere-zero Zk-flows of G. We give a description of the modular flow polynomial in terms of (open) Ehrhart polynomials of lattice polytopes. Using Ehrhart–Macdonald reciprocity we give a combinatorial interpretation for the values of φG at negative arguments which answers a question of Beck and Zaslavsky (Adv Mat...

The Hannay-Ozorio de Almeida sum formula is a useful principle in the study of the distribution of closed orbits for Hamiltonian flows [7]. Roughly speaking, it asserts that an appropriately weighted sum of measures supported on periodic orbits converges to the physical measure as the periods become large. This formula was originally introduced and used in the study of Quantum Chaos. In particu...

In this paper we prove that the Benjamin–Ono equation admits an analytic Birkhoff normal form in open neighborhood of zero H0s(T,R) for any s>−1/2 where denotes subspace Sobolev space Hs(T,R) elements with mean 0. As application show −1/2<s<0, flow map S0t:H0s(T,R)→H0s(T,R) is nowhere locally uniformly continuous a H0s(T,R).

Nowhere dense classes of graphs [21, 22] are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness, a concept originating in finite model theory, has proved to be particularly useful. Uniform quasi-wideness is used in many fpt-algorithms on nowher...

Marginal AMP chain graphs are a recently introduced family of models that is based on graphs that may have undirected, directed and bidirected edges. They unify and generalize the AMP and the multivariate regression interpretations of chain graphs. In this paper, we present a constraint based algorithm for learning a marginal AMP chain graph from a probability distribution which is faithful to ...

‎In this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $C_4$-free.‎

The investigation of impact of fuzzy sets on zero forcing set is the main aim of this paper. According to this, results lead us to a new concept which we introduce it as Fuzzy Zero Forcing Set (FZFS). We propose this concept and suggest a polynomial time algorithm to construct FZFS. Further more we compute the propagation time of FZFS on fuzzy graphs. This concept can be more efficient to model...