
Structural Parameterizations of Clique Coloring
A clique coloring of a graph is an assignment of colors to its vertices ...
read it

The Algorithmic Complexity of TreeClique Width
Treewidth has been proven to be a useful parameter to design fast and e...
read it

Target Set Selection Parameterized by CliqueWidth and Maximum Threshold
The Target Set Selection problem takes as an input a graph G and a nonn...
read it

Towards exact structural thresholds for parameterized complexity
Parameterized complexity seeks to use input structure to obtain faster a...
read it

CliqueWidth and Directed Width Measures for AnswerSet Programming
Disjunctive Answer Set Programming (ASP) is a powerful declarative progr...
read it

On tradeoffs between width and filllike graph parameters
In this work we consider two twocriteria optimization problems: given a...
read it

Potential Maximal Cliques Parameterized by Edge Clique Cover
We show that the number of minimal separators on graphs with edge clique...
read it
Maximizing Happiness in Graphs of Bounded CliqueWidth
Cliquewidth 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 cliquewidth 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 NPcomplete on threshold graphs. Hence, it is not even in XP when parameterized by cliquewidth, since threshold graphs have cliquewidth at most two. As a complement for this result we provide a n^O(ℓ·cw) algorithm for MHE, where ℓ is the number of colors and cw is the cliquewidth of the input graph. We also construct an FPT algorithm for MHV with running time O^*((ℓ+1)^O(cw)), where ℓ is the number of colors in the input. Additionally, we show O(ℓ n^2) algorithm for MHV on interval graphs.
READ FULL TEXT VIEW PDF
Comments
There are no comments yet.