On Happy Colorings, Cuts, and Structural Parameterizations

  • Ivan Bliznets
  • Danil SagunovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11789)


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.


Happy coloring Maximum happy vertices Maximum happy edges Homophily law Multiway cut Distance to triviality Treewidth Clique-width Parameterized complexity 


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Authors and Affiliations

  1. 1.St. Petersburg Department of Steklov Institute of Mathematics of the Russian Academy of SciencesSt. PetersburgRussia
  2. 2.National Research University Higher School of EconomicsSt. PetersburgRussia

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