Exercise · ZW-BIPARTITE-GRAPH-001 · ★☆☆ Basic
Which of the following graphs is bipartite?
Choose one option.
Show answer
- C. \(C_6\), the cycle on 6 vertices
Explanation
The vertices of \(C_6\) alternate between \(A\) and \(B\) around the cycle, and since 6 is even it closes with no conflict. \(C_5\), \(K_3\) and \(K_4\) contain odd cycles.
Review the concept: Bipartite graph
A bipartite graph is a graph \(G=(V,E)\) whose vertices split into two disjoint sets \(A\) and \(B\) so that every edge \(e\in E\) joins a vertex of \(A\) to one of \(B\).
\[V=A\cup B,\quad A\cap B=\varnothing,\quad |e\cap A|=1\ \text{ for every } e\in E\]
More practice problems: bipartite graph
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