Computer Science · Graph Matching
Which of the following statements accurately characterizes a Maximum Matching in graph theory?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It is a locally maximum set of non-adjacent edges that simply cannot be enlarged by adding another edge without violating the matching property.
- 2It strictly guarantees that every single vertex within the graph is covered by an edge, a condition that mandates the graph possesses an even number of vertices.
- 3It is mathematically defined as a matching where any locally maximal selection of edges automatically qualifies as the globally optimal selection regardless of the graph's structure.
- 4It represents the globally optimal selection that contains the largest possible number of edges among all matchings; while it is inherently maximal, a maximal matching is not necessarily a maximum matching.✓
Correct answer
It represents the globally optimal selection that contains the largest possible number of edges among all matchings; while it is inherently maximal, a maximal matching is not necessarily a maximum matching.
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