The problem of computing a maximal planar subgraph of a non planar graph has been deeply investigated over the last 20 years. Several attempts have been tried to solve the problem with the help of P Q-trees. The latest attempt has been reported by Jayakumar et al. 10]. In this paper we show that the algorithm presented by Jayakumar et al. is not correct. We show that it does not necessarily com...

This paper describes an efficient algorithm to find a Hamiltonian circuit in an arbitrary 4-connected maximal planar graph. The algorithm is based on our simlplified version of Whitney's proof of his theorem: every 4-connected maximal planar graph has a Hamiltonian circuit.

A graph is fan-crossing free if it has a drawing in the plane so that each edge crossed by independent edges, crossing edges have distinct vertices. On other hand, common vertex, they form fan. Both are prominent examples for beyond-planar graphs. Further well-known classes k-planar, k-gap-planar, quasi-planar, and right angle We use subdivision, node-to-circle expansion path-addition operation...

Extending the concept of ordered graphs, we propose a new data structure to express rooted planar maps, which is called a planar map pattern. In order to develop an efficient data mining method from a dataset of rooted planar maps, we propose a polynomial time algorithm for finding a minimally generalized planar map pattern, which represents maximal structural features common to rooted planar m...

The number of spanning trees of a map C denoted by τ(C) is the total number of distinct spanning subgraphs of C that are trees. A maximal planar map is a simple graph G formed by n vertices, 3(n − 2) edges and all faces having degree 3 [2]. In this paper, we derive the explicit formula for the number of spanning trees of the maximal planar map and deduce a formula for the number of spanning tre...

A graph is a triangulation if it is planar and every face is a triangle. A triangulation is rooted if the external triangular face is labelled. Two rooted triangulations with the same external face labels are isomorphic if their internal vertices can be labelled so that both triangulations have identical edge lists. In this article, we show that in the set of rooted triangulations on n points w...