A Correction to this paper has been published: 10.1007/s00453-015-0002-1

A “based” plane triangulation is a plane triangulation with one designated edge on the outer face. In this paper we give a simple algorithm to generate all biconnected based plane triangulations with at most n vertices. The algorithm uses O(n) space and generates such triangulations in O(1) time per triangulation without duplications. The algorithm does not output entire triangulations but the ...

Fuzzy planar graph is an important subclass of fuzzy graph. Fuzzy planar graphs and its several properties are presented. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and several properties of it are studied. Isomorphism on fuzzy graphs are well defined in literature. Isomorphic relation between fuzzy planar graph and its dual graph are established.

We show that a vertex based data structure that keeps only pointers per vertex can store triangulations navigate them and maintain them under swap operations By comparison edge based structures such as the winged edge take pointers per vertex and triangle based structures take pointers per vertex Introduction Representations of planar subdivisions are central to applications of geo metric compu...

A drawing of a plane graph is called an inner rectangular drawing if every edge is drawn as a horizontal or vertical line segment so that every inner face is a rectangle. An inner rectangular drawing has some applications to VLSI layouts. In this talk we show that a plane graph G has an inner rectangular drawing D if and only if a new bipartite graph constructed from G has a perfect matching. W...

This paper studies the choosability of signed planar graphs. We prove that every signed planar graph is 5-choosable and that there is a signed planar graph which is not 4-choosable while the unsigned graph is 4-choosable. For each k ∈ {3, 4, 5, 6}, every signed planar graph without circuits of length k is 4-choosable. Furthermore, every signed planar graph without circuits of length 3 and of le...

Geographic routing is a routing paradigm, which uses geographic coordinates of network nodes to determine routes. Greedy routing, the simplest form of geographic routing forwards a packet to the closest neighbor towards the destination. A greedy embedding is a embedding of a graph on a geometric space such that greedy routing always guarantees delivery. A Schnyder drawing is a classical way to ...

An interesting question about planar graphs is whether they admit plane embeddings in which every bounded face is convex. Stein [10] gave as a necessary and sufficient condition that every face boundary be a simple cycle and every two bounded faces meet in a connected set, with an extra condition about the number of vertices on the outer face. Tutte [12] gave a similar characterisation, and lat...

This chapter deals with compressed coding of graphs. We focus on planar graphs, a widely studied class of graphs. A planar graph is a graph that admits an embedding in the plane without edge crossings. Planar maps (class of embeddings of a planar graph) are easier to study than planar graphs, but as a planar graph may admit an exponential number of maps, they give little information on graphs. ...