Using the existence of noncrossing Eulerian circuits in Eulerian plane graphs, we give a short constructive proof of the theorem of Heawood that Eulerian triangulations are 3-colorable.

A straight ahead walk in an embedded Eulerian graph G always passes from an edge to the opposite edge in the rotation at the same vertex A straight ahead walk is called Eulerian if all the edges of the embedded graph G are traversed in this way starting from an arbitrary edge An embedding that contains an Eulerian straight ahead walk is called an Eulerian embedding In this article we characteri...

The closed cone of flag vectors of Eulerian partially ordered sets is studied. It is completely determined up through rank seven. HalfEulerian posets are defined. Certain limit posets of Billera and Hetyei are half-Eulerian; they give rise to extreme rays of the cone for Eulerian posets. A new family of linear inequalities valid for flag vectors of Eulerian posets is given.

in the course of expansion in turbines steam nucleates to become a two-phase mixture, the liquid consisting of a very large number of extremely small droplets carried by the vapor. formation and subsequent behaviour of the liquid lowers the performance of turbine wet stages. the calculations were carried out assuming that the flow is two dimensional, compressible, turbulent and viscous. a class...

A graded partially ordered set is Eulerian if every interval has the same number of elements of even rank and of odd rank. Face lattices of convex polytopes are Eulerian. For Eulerian partially ordered sets, the flag vector can be encoded efficiently in the cd-index. The cd-index of a polytope has all positive entries. An important open problem is to give the broadest natural class of Eulerian ...

An undirected graph is Eulerian if it is connected and all its vertices are of even degree. Similarly, a directed graph is Eulerian, if for each vertex its in-degree is equal to its out-degree. It is well known that Eulerian graphs can be recognized in polynomial time while the problems of finding a maximum Eulerian subgraph or a maximum induced Eulerian subgraph are NP-hard. In this paper, we ...

Consider an undirected Eulerian graph, a graph in which each vertex has even degree. An Eulerian orientation of the graph is an orientation of its edges such that for each vertex v, the number of incoming edges of v equals to outgoing edges of v, i.e. din(v) = dout(v). Let P0 denote the set of all Eulerian orientations of graph G. In this paper, we are concerned with the questions of sampling u...

We derive a non-dimensional metric to quantify the expected Lagrangian persistence of objectively defined Eulerian vortices in two-dimensional unsteady flows. This persistence metric is the averaged deviation of the vorticity from its spatial mean over the Eulerian vortex, normalized by the instantaneous material leakage from the Eulerian vortex. The metric offers a modeland frame-independent t...

Problems involving a transition between dense and dilute dispersed phase regimes often require hybridization of Eulerian-Eulerian (EE) Eulerian-Lagrangian (EL) methods for accurate efficient computational modeling. A hybrid EE-EL formulation is developed in this work from first principles, which asymptotes to well-established EE EL limiting conditions. smooth dynamic criterion corresponding alg...

Sum-free enumerative formulae are derived for several classes of rooted planar maps with no vertices of odd valency (eulerian maps) and with two vertices of odd valency (unicursal maps). As corollaries we obtain simple formulae for the numbers of unrooted eulerian and unicursal planar maps. Also, we obtain a sum-free formula for the number of rooted bi-eulerian (eulerian and bipartite) maps and...