How to find even or odd cylce in a graph

Question

Consider this example , There is even vertices cycle as well as odd vertices cycle as per my understanding, let me know if it correct.

Thanks a lot

Comments

yes, here exist atleast a cycle with odd no.of vertices and there exist atleast a cycle with even no.of vertices.

 

name them as A,B,C,D,E,F,G,H,I as row by row

A-B-C-F-E-H-G-D-A ------> cycle with EVEN no.of vertices

A-B-C-F-I-A ----->  cycle with ODD no.of vertices

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thanks a lot for your response, if we have odd and even cycles in a same graph then it will require 4-colors to color its vertices, is it correct ?

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No, using 3 color you can color the graph