Theorem 7. Let G be a planar graph with. If any 6-cycle contains at most one chord, then G is of class 1. Proof. Suppose that G is a counterexample to our theorem with the minimum number of edges and ...

However, the main source of inspiration for planar graphs was the Four Color Conjecture (now Theorem; cf. Chapter 8) that the vertices of any planar graph can be colored with four colors in such a way ...

Graph Colouring: The process of assigning colours to elements of a graph, typically vertices, so that adjacent elements receive different colours.

As a basis of dealing with various constraints arising in IC layout problems we present efficient algorithms for planar embedding of graphs with constraints on vertices in placing them on face ...

Planar graph: A graph that can be embedded in the plane without any of its edges crossing. Distance query: A computation request that involves determining the shortest path or minimum distance ...

Solving the general planar graph colouring problem using Grover's Algorithm. The backtracking algorithm takes O (k^n) for k colours and n vertices while Grover's reduces this complexity to O (sqrt ...

Given a graph G = (V, E), a coloring of a graph consists in assigning a color to any vertex of the graph, such that any pair of neighboring vertices receives different colors. Finding the minimum ...