4. Problem. Characterize those graphs G for which L(G) is hamiltonian. This class of graphs includes both the eulerian and hamiltonian graphs. (The problems of conveniently …

in with Eulerian and Lagrangian coordinates. The Eulerian coord nate (x; t) is the physical space plus time. The Eulerian description of the flow is to describe the flow using quantities as a …

In the following G = (V; E) denotes a nite directed graph, with loops and multiple edges permitted. An Eulerian tour of G is a closed path that traverses each directed edge exactly once. Such a …

The main idea in our proof is to study the Euler characteristic of a particularly nice family of graphs. Recall that a graph has an Eulerian tour iff there exists a path that starts and ends at …

Proof 1: Assume G has an Eulerian cycle. Traverse the cycle removing edges as they are traversed. Every vertex maintains its parity, as the traversal enters and exits the vertex, since …

A tour is Eulerian if every edge of D occurs at least once (and hence exactly once). A digraph which has no isolated vertices and contains an Eulerian tour is called an Eulerian digraph. …

We’ll see below that the converse of Lemma 3.3.A also holds and that a connected graph is Eulerian if and only if it is even. The fact that G is even is sufficient for G to be Eulerian is …