We study the equivalence relation on the set of acyclic orientations of an undirected graph Γ generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in tur...

Given a graph G we provide dynamic programming algorithms for many locally checkable vertex subset and vertex partitioning problems. Their runtime is polynomial in the number of equivalence classes of problem-specific equivalence relations on subsets of vertices, defined on a given decomposition tree of G. Using these algorithms all these problems become solvable in polynomial time for many wel...

the aim of this paper is to study co-prolongations of central extensions. we construct the obstruction theory forco-prolongations and classify the equivalence classes of these by kernels of homomorphisms between 2-dimensional cohomology groups of groups.

We consider the equivalence classes of graphs induced by the unsigned versions of the Reidemeister moves on knot diagrams. Any graph which is reducible by some finite sequence of these moves, to a graph with no edges is called a knot graph. We show that the class of knot graphs strictly contains the set of delta-wye graphs. We prove that the dimension of the intersection of the cycle and cocycl...

let $g$ be a simple graph of order $n$ and size $m$.the edge covering of $g$ is a set of edges such that every vertex of $g$ is incident to at least one edge of the set. the edge cover polynomial of $g$ is the polynomial$e(g,x)=sum_{i=rho(g)}^{m} e(g,i) x^{i}$,where $e(g,i)$ is the number of edge coverings of $g$ of size $i$, and$rho(g)$ is the edge covering number of $g$. in this paper we stud...

The paper considers the problem of learning classes of graphs closed under taking minors It is shown that any such class can be properly learned in polynomial time using membership and equivalence queries The representation of the class is in terms of a set of minimal excluded minors obstruction set

Indiana University and the University of Washington 2Chain graphs (CG) (= adicyclic graphs) use undirected and directed edges to represent simultaneously both structural and associative dependences.. Like acyclic directed graphs (ADGs), the CG associated with a given statistical model may not be unique, so CGs fall into Markov equivalence classes, which may be superexponentially large, leading ...