Describing faces in plane triangulations

Good Triangulations in Plane

Braced edges in plane triangulations

A plane triangulation is an embedding of a maximal planar graph in the Euclidean plane. Foulds and Robinson (1979) first studied the problem of transforming one triangulation to another by a sequence of diagonal operations. where a diagonal operation deletes one edge and inserts the other diagonal of the resulting quadrilateral face. An edge which cannot be removed by a single diagonal operatio...

h-perfect plane triangulations

We characterise t-perfect plane triangulations by forbidden induced subgraphs. As a consequence, we obtain that a plane triangulation is h-perfect if and only if it is perfect.

Hamilton cycles in plane triangulations

We extend Whitney’s Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely we define a decomposition of a plane triangulation G into 4-connected ‘pieces’ and show that if each piece shares a triangle with at most three other pieces then G is hamiltonian. We provide an example to show that our hypothesis that ‘each...

Plane triangulations are 6-partitionable

Given a graph G = (V; E) and k positive integers n1; n2; : : : ; nk such that ∑k i=1 ni = |V |, we wish to 2nd a partition P1; P2; : : : ; Pk of the vertex set V such that |Pi| = ni and Pi induces a connected subgraph of G for all i; 16 i6 k. Such a partition is called a k-partition of G. A graph G with n vertices is said to be k-partitionable if there exists a k-partition of G for any partitio...