Exercise · ZW-GRAPH-COLORING-005 · ★☆☆ Basic
The graph has vertices \(1,2,3,4\) and edges \(\{1,2\},\{2,3\},\{1,3\},\{3,4\}\). Which is a proper coloring?
Choose one option.
Show answer
- C. 1: red, 2: green, 3: blue, 4: red
Explanation
Every edge must get two different colors. In the correct one, \(\{3,4\}\) is blue-red. The others repeat a color on \(\{1,3\}\), \(\{3,4\}\) or \(\{1,2\}\).
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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