We want to find out in which cases the closed trail C0 constructed in Example 2.1.2 (2) is already necessarily Eulerian. An Eulerian graph is called arbitrarily traceable from v0 if each maximal trail beginning in v0 is an Euler tour; here maximal means that all edges incident with the end vertex of the trail occur in the trail. Prove the following results due to Ore (who introduced the concept of arbitrarily traceable graphs [Ore51]) and to [Bae53] and [ChWh70].
(a) G is arbitrarily traceable from v0 if and only if G v0 is acyclic.
(b) If G is arbitrarily traceable from 
, then is a vertex of maximal degree.
(c) If G is arbitrarily traceable from at least three different vertices, then G is a cycle.
(d) There exist graphs which are arbitrarily traceable from exactly two vertices; one may also prescribe the degree of these vertices.