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- W2965619982 abstract "Abstract A graph is H -free if it contains no induced subgraph isomorphic to H . We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in polynomial time on $$(sP_1+ P_3)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -free graphs for every integer $$sge 1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> . We show the same result for the variants Connected Feedback Vertex Set and Connected Odd Cycle Transversal . We also prove that the latter two problems are polynomial-time solvable on cographs; this was already known for Feedback Vertex Set and Odd Cycle Transversal . We complement these results by proving that Odd Cycle Transversal and Connected Odd Cycle Transversal are -complete on $$(P_2+ P_5,P_6)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>5</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -free graphs." @default.
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- W2965619982 date "2020-04-29" @default.
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- W2965619982 title "On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest" @default.
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