On face vectors and vertex vectors of convex polyhedra
Discrete Mathematics
Realizations with a cut-through Eulerian circuit
Discrete Mathematics
Dual Eulerian Properties of Plane Multigraphs
SIAM Journal on Discrete Mathematics
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On plane graphs with link component number equal to the nullity
Discrete Applied Mathematics
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A Petrie walk in a plane graph G is obtained by walking on edges of G, alternatingly selecting as next edge the left edge and the right edge of the current edge in the rotation of edges around the common vertex. We give a characterization of 4-valent plane graphs with Eulerian Petrie walks, which gives rise to a simple algorithm for constructing such graphs. This algorithm is then used to answer the question whether or not there exist 4-valent plane graphs with Eulerian Petrie walks and faces of prescribed sizes.