Traditional representations of graphs and their duals suggest the requirement that the dual vertices should be placed inside their corresponding primal faces, and the edges of the ...
A dual-eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an euler circuit in the dual grap...
We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given...
We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n2 )×O(n2 ) grid, with at most three bends per edge, where n is the number of verti...
: Let G be a 3-connected planar graph and G∗ be its dual. We show that the pathwidth of G∗ is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth...