Exercise · ZW-BIPARTITE-GRAPH-004 · ★☆☆ Basic
Which of these conditions guarantees that a graph is NOT bipartite?
Choose one option.
Show answer
- D. It has a cycle of length 7
Explanation
A graph is bipartite exactly when it has no odd cycles. A 7-cycle rules that out; trees, even cycles and edgeless graphs are bipartite.
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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