Question

This is the Petersen graph: 4 6 8 2 3 (a) Give an argument to show that the Petersen graph does not contain a subdivision of K5. (b) Show that the Petersen graph contains a subdivision of K3,3.

Answer 1

Solo a) Petersen of wou we requond degane 4. 3 no goraph does not does not contain a Subdivision ks. Because, an Ks gotiph there is 5 venter which directly connected to other four Ventices le each Vertex has degoree 4. So, In order to get Subdivision of ks minimum 5 veltices with atleast But an Petersen graph Each Vertex has has maximum deg one So there is possibility of ks. Subdivision, 6) k3,3 is non-planall graph with 6 vertices, which each Vertex Connected to other 3 vertices ire. 6 vertices with minimum 3 i-e. diures connected to directly degree other thorne veutices. So, In make Subdivision of - first Hemove edges (2,3) f (6,9). I Edyes an we required ouder to of k3,3 we
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