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 …

Partial cubes are, by definition, isometric subgraphs of hypercubes. Cubic inflation is an
operation that transforms a 2-cell embedded graph G into a cubic graph embedded in the …

Call i-hedrite any 4-valent n-vertex plane graph, whose faces are 2-, 3-and 4-gons only and
p2+ p3= i. The edges of an i-hedrite, as of any Eulerian plane graph, are partitioned by its …

Consider a closed curve in the plane that does not intersect itself; by the Jordan–Schoenflies
theorem, it bounds a distorted disk. Now consider a closed curve that intersects itself …

We provide a link between topological graph theory and pseudoline arrangements from the
theory of oriented matroids. We investigate and generalize a function f that assigns to each …

An anti-directed walk in a directed graph is a walk in which edge directions alternate. An
Eulerian directed graph is aneulerian if it contains a closed antidirected walk passing …

CUBIC INFLATION, MIRROR GRAPHS, REGULAR MAPS, AND PARTIAL CUBES Page 1
University of Ljubljana Institute of Mathematics, Physics and Mechanics Department of …