2 votes 2 votes What is the smallest number of colors that can be used to color the vertices of a cube so that no two adjacent vertices are colored identically? Graph Theory go2025-dm-4 numerical-answers graph-coloring + – gatecse asked Sep 14, 2020 • recategorized Sep 14, 2020 by Lakshman Bhaiya gatecse 138 views answer comment Share Follow See 1 comment See all 1 1 comment reply Nikhil_dhama commented Dec 30, 2020 reply Follow Share https://gateoverflow.in/346160/go-2021-discrete-mathematics-4-5 Both are same. 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes With $2$ colors we can do coloring as shown below. We can also see that there are no cycles of an odd length in this graph and hence it is $2-$ colorable. gatecse answered Sep 14, 2020 • edited Sep 14, 2020 by soujanyareddy13 gatecse comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes A hypercube or k-dimensional cube (Qk) is also a bipartite graph and every bipartite graph has chromatic number <= 2 . So for the given graph min number of colors (chromatic number) required is 2 . Isha_99 answered Dec 16, 2021 Isha_99 comment Share Follow See all 0 reply Please log in or register to add a comment.
