Graph Theory: Lecture No. 16
Let Gbe a graph with maximum degree ∆.
Then ∆≤χ0(G)≤∆ + 1.
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Graph Theory: Lecture No. 16 - Maximum Degree, Planar Graphs, and Euler's Formula, Slides of Design Patterns
This document from graph theory: lecture no. 16 covers the maximum degree of a graph, plane graphs, euler's formula, and the fact that a planar graph is 6-colorable. Learn about the relationships between the number of vertices, edges, and faces in a plane graph.
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2012/2013
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Let G be a graph with maximum degree ∆. Then ∆ ≤ χ′(G ) ≤ ∆ + 1.
A graph drawn on the plane in such way that no two edges intersect other than at the end points is called a plane graph. Abstract graphs that can be drawn in this way are called planar.
A plane graph with n ≥ 3 vertices has at most 3 n − 6 edges.
A planar graph is 6 -colorable.