We show that if C is a class of graphs which is nowhere dense then rst-order model-checking is xed-parameter tractable on C. As all graph classes which exclude a xed minor, or are of bounded local tree-width or locally exclude a minor are nowhere dense, this generalises algorithmic meta-theorems obtained for these classes in the past (see [11, 13, 4]). Conversely, if C is not nowhere dense and ...

We present a common generalization of counting lattice points in rational polytopes and the enumeration of proper graph colorings, nowhere-zero flows on graphs, magic squares and graphs, antimagic squares and graphs, compositions of an integer whose parts are partially distinct, and generalized latin squares. Our method is to generalize Ehrhart’s theory of lattice-point counting to a convex pol...

This article considers transient flows for planar contractions and Oldroyd-B fluids, with increasing flow-rate boundary conditions. We employ a novel hybrid finite volume/element time-dependent algorithm. The hybrid scheme consists of a TaylorGalerkin finite element discretisation, and a cell-vertex fluctuation-distribution finite volume approach. These two approaches are coupled at each time-s...

We provide a new class of matrices, called binet matrices (denoted by B), which guarantee half-integral vertices for the polytope P = fx : l x u; a Bx bg. They furnish a direct generalisation of totally unimodular network matrices and arise from the node-edge incidence matrices of bidirected graphs in the same way as the network matrices do from directed graphs. We develop the necessary theory ...

‎in this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $c_4$-free.‎

In a previous work, we gave a coalgebraic framework of directed graphs equipped with weights (or probability vectors) in terms of (Markov) L-coalgebras. They are K-vector spaces equipped with two co-operations, ∆M , ∆̃M verifying, (∆̃M ⊗ id)∆M = (id⊗∆M)∆̃M . In this paper, we study the category of L-algebras (dual of L-coalgebras), prove that the free L-algebra on one generator is constructed over...

We introduce a new family of graphical models that consists of graphs with possibly directed, undirected and bidirected edges but without directed cycles. We show that these models are suitable for representing causal models with additive error terms. We provide a set of sufficient graphical criteria for the identification of arbitrary causal effects when the new models contain directed and und...

We use K∗ n to denote the bidirected complete graph on n vertices. A nomadic Hamiltonian decomposition of K∗ n is a Hamiltonian decomposition, with the additional property that “nomads” walk along the Hamiltonian cycles (moving one vertex per time step) without colliding. A nomadic near-Hamiltonian decomposition is defined similarly, except that the cycles in the decomposition have length n − 1...

Abstract. Proper vertex colorings of a graph are related to its boundary map, also called its signed vertex-edge incidence matrix. The vertex Laplacian of a graph, a natural extension of the boundary map, leads us to introduce nowhere-harmonic colorings and analogues of the chromatic polynomial and Stanley’s theorem relating negative evaluations of the chromatic polynomial to acyclic orientatio...