Let G be a connected simple graph in which all vertices have degree 4. Prove that it is possible to color the edges of G red or blue so that every vertex is adjacent to two red edges and two blue edges. Hint: Start by showing that G has a closed Eulerian walk.

Let G be a connected simple graph in which all vertices have degree 4. Prove that it is possible to color the edges of G red or blue so that every vertex is adjacent to two red edges and two blue edges. Hint: Start by showing that G has a closed Eulerian walk.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let G be a connected simple graph in which all vertices have degree 4. Prove that it is possible to color the edges of G red or blue so that
every vertex is adjacent to two red edges and two blue edges. Hint: Start by showing that G has a closed Eulerian walk.

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