0 votes 0 votes 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 Graph Theory graph-coloring + – ejaz asked Jun 30, 2018 ejaz 493 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Shaik Masthan commented Jun 30, 2018 reply Follow Share 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 0 votes 0 votes ejaz commented Jun 30, 2018 reply Follow Share 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 ? 0 votes 0 votes rajatmyname commented Aug 15, 2018 reply Follow Share No, using 3 color you can color the graph 0 votes 0 votes Please log in or register to add a comment.