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Partitioning sparse graphs into an independent set and a graph with bounded size components

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Academic year: 2021

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Figure 2: A planar graph with girth 5 and maximum degree 3 that forces colour I on the 2-vertex in every (I, P 3 )-partition.
Figure 3: A planar graph with girth 7 and maximum degree 4 that has no (I, P 3 )-partition.

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