Exercise · ZW-GRAPH-COLORING-001 · ★☆☆ Basic
What is the minimum number of colors in a proper coloring of the complete graph \(K_5\)?
Choose one option.
Show answer
- D. 5
Explanation
In \(K_5\) every two vertices are adjacent, so no color can repeat: 5 are needed.
Review the concept: Graph coloring
A proper coloring \(c\) with \(k\) colors of a graph \(G=(V,E)\) assigns to each vertex one of the colors \(1,\dots,k\) so that no two adjacent vertices share a color.
\[c:V\to\{1,\dots,k\},\qquad c(u)\neq c(v)\ \text{ if } \{u,v\}\in E\]
More practice problems: graph coloring
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