Euler paths in series parallel graphs
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A polynomial time algorithm for determining zero Euler---Petrie genus of an Eulerian graph
Discrete Mathematics - Algebraic and topological methods in graph theory
Plane graphs with Eulerian Petrie walks
Discrete Mathematics - Algebraic and topological methods in graph theory
Finding Double Euler Trails of Planar Graphs in Linear Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
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A plane multigraph is said to be dual Eulerian if both itself and its dual contain an Euler path or circuit and the Euler paths have corresponding edge sequences. In this paper several properties of plane multigraphs are derived, and a necessary and sufficient condition for a plane multigraph to be dual Eulerian is given. Although the necessary and sufficient condition for a multigraph to be Eulerian is somewhat trivial, the necessary and sufficient condition for a plane multigraph to be dual Eulerian is not. Nevertheless, the question of whether or not a plane multigraph is dual Eulerian can be answered in time proportional to a linear function of the number of edges of the graph, and an algorithm that answers this question is presented in this paper. This theory can be applied to the layout synthesis of functional cells for Complementary Metal-Oxide Semiconductor Very Large-Scale Integrated circuits.