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- W4296900537 abstract "Abstract In the NP-hard Colored ( s , t )- Cut problem, the input is a graph G = ( V , E ) together with an edge-coloring ℓ : E → C , two vertices s and t , and a number k . The question is whether there is a set $Ssubseteq C$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>S</mml:mi> <mml:mo>⊆</mml:mo> <mml:mi>C</mml:mi> </mml:math> of at most k colors such that deleting every edge with a color from S destroys all paths between s and t in G . We continue the study of the parameterized complexity of Colored ( s , t )- Cut . First, we consider parameters related to the structure of G . For example, we study parameterization by the number ξ i of edge deletions that are needed to transform G into a graph with maximum degree i . We show that Colored ( s , t )- Cut is W[2]-hard when parameterized by ξ 3 , but fixed-parameter tractable when parameterized by ξ 2 . Second, we consider parameters related to the coloring ℓ . We show fixed-parameter tractability for three parameters that are potentially smaller than the total number of colors | C | and provide a linear-size problem kernel for a parameter related to the number of edges with rare edge colors." @default.
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- W4296900537 date "2022-09-22" @default.
- W4296900537 modified "2023-09-27" @default.
- W4296900537 title "Refined Parameterizations for Computing Colored Cuts in Edge-Colored Graphs" @default.
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- W4296900537 doi "https://doi.org/10.1007/s00224-022-10101-z" @default.
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