Graph homomorphism, and how to proof?

325 Views Asked by Bumbble Comm At 04 May 2026 - 8:16

I want to know whether there exists a homomorphism from this graph (below in the image) to $K_5$ (complete graph with 5 vertices).
If so, how can I prove this relationship? Since homomorphism is a new concept to me, I can not easily find a function mapping according to the definition of homomorphism.

enter image description here

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Bumbble Comm On 23 Aug 2014 - 8:17 BEST ANSWER

EDIT: Apologize since I've mistook this graph as a planar graph. But this graph admits a four-coloring: enter image description here