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- W3116493424 abstract "Clique-width is one of the most important parameters that describes structural complexity of a graph. Probably, only treewidth is more studied graph width parameter. In this paper we study how clique-width influences the complexity of the Maximum Happy Vertices (MHV) and Maximum Happy Edges (MHE) problems. We answer a question of Choudhari and Reddy ’18 about parameterization by the distance to threshold graphs by showing that MHE is (mathrm {NP})-complete on threshold graphs. Hence, it is not even in (mathrm {XP}) when parameterized by clique-width, since threshold graphs have clique-width at most two. As a complement for this result we provide a (n^{mathcal {O}(ell cdot mathrm {cw})}) algorithm for MHE, where (ell ) is the number of colors and (mathrm {cw}) is the clique-width of the input graph. We also construct an (mathrm {FPT}) algorithm for MHV with running time (mathcal {O}^*((ell +1)^{mathcal {O}(mathrm {cw})})), where (ell ) is the number of colors in the input. Additionally, we show (mathcal {O}(ell n^2)) algorithm for MHV on interval graphs." @default.
- W3116493424 created "2021-01-05" @default.
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- W3116493424 date "2020-01-01" @default.
- W3116493424 modified "2023-09-27" @default.
- W3116493424 title "Maximizing Happiness in Graphs of Bounded Clique-Width" @default.
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- W3116493424 doi "https://doi.org/10.1007/978-3-030-61792-9_8" @default.
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