R O M A
نویسندگان
چکیده
An upward embedding of an embedded planar graph states, for ea h vertex v, whi h edges are in ident to v \above" or \below" and, in turn, indu es an upward orientation of the edges. In this paper we hara terize the set of all upward embeddings and orientations of a plane graph by using a simple ow model. We take advantage of su h a ow model to ompute upward orientations with the minimum number of sour es and sinks of 1onne ted graphs. Our theoreti al results allow us to easily ompute visibility representations of 1onne ted graphs while having a ertain ontrol over the width and the height of the omputed drawings, and to deal with partial assignments of the upward embeddings \underlying" the visibility representations. 2 1 Introdu tion Let G be an undire ted planar graph with a given planar embedding. Loosely speaking, an upward embedding (also alled an upward representation) of G is given by splitting, for ea h vertex v of G, the ordered ir ular list of the edges that are in ident to v into two linear lists Labove(v) and Lbelow(v), in su h a way that there exists a planar drawing of G with the following properties: (i) all the edges are monotoni ally in reasing in the verti al dire tion; (ii) for ea h vertex v the edges in Labove(v) (Lbelow(v)) are in ident to v above (below) the horizontal line through v. Drawing is said to be an upward drawing of G. An orientation of all edges of from bottom to top de nes an orientation of all edges of G, whi h we all an upward orientation of G. Hen e, any upward embedding of G indu es an upward orientation of G. Figure 1 shows an upward embedding of a plane graph and the upward orientation indu ed by it.
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