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The forest-path partition conjecture for planar graphs without 4-cycles and 6-cycles
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Forest-path partition conjecture. Every planar graph without $4$ -cycles and $6$ -cycles has an $(\mathcal{F}_1,\mathcal{F})$ -partition.
openforest-coloring graph-partitions planar-graphs
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The forest-path partition conjecture for planar graphs without 4-cycles and 6-cycles