4,435 research outputs found
Parameterized Complexity of Equitable Coloring
A graph on vertices is equitably -colorable if it is -colorable and
every color is used either or times.
Such a problem appears to be considerably harder than vertex coloring, being
even for cographs and interval graphs.
In this work, we prove that it is for block
graphs and for disjoint union of split graphs when parameterized by the number
of colors; and for -free interval graphs
when parameterized by treewidth, number of colors and maximum degree,
generalizing a result by Fellows et al. (2014) through a much simpler
reduction.
Using a previous result due to Dominique de Werra (1985), we establish a
dichotomy for the complexity of equitable coloring of chordal graphs based on
the size of the largest induced star.
Finally, we show that \textsc{equitable coloring} is when
parameterized by the treewidth of the complement graph
Parameterized Approximation Schemes using Graph Widths
Combining the techniques of approximation algorithms and parameterized
complexity has long been considered a promising research area, but relatively
few results are currently known. In this paper we study the parameterized
approximability of a number of problems which are known to be hard to solve
exactly when parameterized by treewidth or clique-width. Our main contribution
is to present a natural randomized rounding technique that extends well-known
ideas and can be used for both of these widths. Applying this very generic
technique we obtain approximation schemes for a number of problems, evading
both polynomial-time inapproximability and parameterized intractability bounds
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