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On Happy Colorings, Cuts, and Structural Parameterizations

P. 148–161.
Bliznets I., Sagunov D.

We study the Maximum Happy Vertices and Maximum Happy Edges problems. The former problem is a variant of clusterization, where some vertices have already been assigned to clusters. The second problem gives a natural generalization of Multiway Uncut, which is the complement of the classical Multiway Cut problem. Due to their fundamental role in theory and practice, clusterization and cut problems has always attracted a lot of attention. We establish a new connection between these two classes of problems by providing a reduction between Maximum Happy Vertices and Node Multiway Cut. Moreover, we study structural and distance to triviality parameterizations of Maximum Happy Vertices and Maximum Happy Edges. Obtained results in these directions answer questions explicitly asked in four works: Agrawal ’17, Aravind et al. ’16, Choudhari and Reddy ’18, Misra and Reddy ’17.

Language: English
DOI
Text on another site
Keywords: parameterized complexityHappy coloringHomophily lawClique-width

In book

Graph-Theoretic Concepts in Computer Science 45th International Workshop, WG 2019, Vall de Núria, Spain, June 19–21, 2019, Revised Papers
Bliznets I. Vol. 11789: Lecture Notes in Computer Science. , Springer, 2019.
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