Grid Embedding of 4-Connected Plane Graphs

Grid Drawings of Four-Connected Plane Graphs

A grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on plane grid points and all edges are drawn as straight line segments between their endpoints without any edge-intersection. In this paper we give a very simple algorithm to find a grid drawing of any given 4-connected plane graph G with four or more vertices on the outer face. The algorithm take...

Convex Grid Drwaings of Four-Connected Plane Graphs

A convex grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on grid points, all edges are drawn as straight-line segments between their endpoints without any edge-intersection, and every face boundary is a convex polygon. In this paper we give a linear-time algorithm for finding a convex grid drawing of any 4-connected plane graph G with four or mor...

2-edge-Hamiltonian-connectedness of 4-connected plane graphs

A graph G is called 2-edge-Hamiltonian-connected if for any X ⊂ {x1x2 : x1, x2 ∈ V (G)} with 1 ≤ |X| ≤ 2, G ∪ X has a Hamiltonian cycle containing all edges in X, where G ∪ X is the graph obtained from G by adding all edges in X. In this paper, we show that every 4-connected plane graph is 2edge-Hamiltonian-connected. This result is best possible in many senses and an extension of several known...

Acute triangles in 4-connected maximal plane graphs

In this paper, we show that every 4-connected maximal plane graph with m finite faces other than the octahedron can be drawn in the plane so that at least (m+3)/2 faces are acute triangles. Moreover, this bound is sharp. © 2005 Published by Elsevier B.V.

Optimal Orthogonal Drawings of Connected Plane Graphs