Phase transitions inXYantiferromagnets on plane triangulations

Good Triangulations in Plane

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.

On light cycles in plane triangulations

A subgraph of a plane graph is light if each of its vertices has a small degree in the entire graph. Consider the class ~¢-(5) of plane triangulations of minimum degree 5. It is known that each G C,Y-(5) contains a light triangle. From a recent result of Jendrol' and Madaras the existence of light cycles C4 and C5 in each G C.~(5) follows. We prove here that each G E.Y-(5) contains also light c...

On covering bridged plane triangulations with balls

We show that every plane graph of diameter 2r in which all inner faces are triangles and all inner vertices have degree larger than 5 can be covered with two balls of radius r : 2003 Wiley Periodicals, Inc. J Graph Theory 44:

On 3-coloring of plane triangulations

Let G be a plane triangulation. For a color-assignment λ : V (G) → {1, 2, 3}, a face of G whose vertices receive all three colors is called a vivid face with respect to λ. Let hλ(G) be the number of vivid faces in G with respect to λ. Let C(G) be the set of 3-color-assignments of G and let G(n) be the set of plane triangulations with n faces. Let h(G) = max{hλ(G) : λ ∈ C(G)} and h(n) = min{h(G)...