Graph Theory: Lecture No. 17
A planar graph is 6-colorable.
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Graph Theory: Lecture No. 17 - Planarity and Colorability, Slides of Design Patterns
The concepts of planarity and colorability in graph theory as presented in lecture notes. The notes discuss kuratowski's theorem, which establishes the equivalence of planarity with the absence of certain forbidden minors, and the relationship between maximum degree and topological minors. Additionally, the notes touch upon the fact that every face in a 2-connected plane graph is bounded by a cycle.
Typology: Slides
2012/2013
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A planar graph is 6 -colorable.
A planar graph is 5 -colorable.
If ∆(X ) ≤ 3 then every MX contains a TX. Thus every minor with maximum degree at most 3 is also its topological minor.
A graph contains K 5 or K 3 , 3 as a minor if and only if it contains K 5 or K 3 , 3 as a topological minor.