Does a connected bipartite graph $G=(X \cup Y; E)$ such that $|X|=4$, $|Y|=3$, $|E|=5$ exist? Is there a way to know? Thanks!
2026-03-28 11:52:55.1774698775
connected bipartite graph exists
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An undirected graph with $n$ nodes needs at least $n-1$ edges to be connected. Any additional structural constraints (e.g., bipartite) will not decrease that requirement.
You have 7 nodes, so you need at least 6 edges. 5 will not work.
See also this: https://stackoverflow.com/questions/27104787/give-the-minimum-and-the-maximum-number-of-edges-in-an-undirected-connected-grap/42600711