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of induced paths into which the vertices of the graph may be partitioned, and the closely related path cover number of is the smallest number of induced paths that together include all vertices of . The girth of a graph is the length of its shortest cycle, but this cycle must be an induced cycle as any chord could be used to produce a shorter cycle; for similar reasons the odd girth of a graph is also the length of its shortest odd induced cycle.

Example

The illustration

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