A closed walk in a connected graph G that contains every edge of G exactly once is an Eulerian circuit. A graph is Eulerian if it contains an Eulerian circuit. It is well known that a connected graph G is Eulerian if and only if every vertex of G is even. An Eulerian walk in a connected graph G is a closed walk that contains every edge of G at least once, while an irregular Eulerian walk in G i...

Here presented is the interrelationship between Eulerian polynomials, Eulerian fractions and Euler-Frobenius polynomials, Euler-Frobenius fractions, Bsplines, respectively. The properties of Eulerian polynomials and Eulerian fractions and their applications in B-spline interpolation and evaluation of Riemann zeta function values at odd integers are given. The relation between Eulerian numbers a...

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.

this work investigates the response of two-dimensional, turbulent boundary layer characteristics over a flat plate to the presence of suspended particulate matter. both phases are assumed to be interacting continua. that is, the carrier fluid equations are considered to be coupled with the particle-phase equations. a finite-difference technique with non-uniform grid has been employed for the so...

Atmospheric dispersion is a topic of great importance especially in relation to pollutant transport. Two different approaches, known as the Eulerian and the Lagrangian frameworks, are used to describe this process. In the Eulerian framework, statistical properties are calculated in a fixed reference frame. This approach is most commonly used in field experiments as well as in laboratory experim...

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 ...

We describe an Eulerian path approach to the DNA fragment assembly that was originated by Idury and Waterman 1995, and then advanced by Pevzner et al. 2001b. This combinatorial approach bypasses the traditional “overlap-layout-consensus” approach and successfully resolved some of the troublesome repeats in practical assembly projects. The assembly results by the Eulerian path approach are accur...