7 research outputs found
Letter graphs and geometric grid classes of permutations: characterization and recognition
In this paper, we reveal an intriguing relationship between two seemingly
unrelated notions: letter graphs and geometric grid classes of permutations. An
important property common for both of them is well-quasi-orderability,
implying, in a non-constructive way, a polynomial-time recognition of geometric
grid classes of permutations and -letter graphs for a fixed . However,
constructive algorithms are available only for . In this paper, we present
the first constructive polynomial-time algorithm for the recognition of
-letter graphs. It is based on a structural characterization of graphs in
this class.Comment: arXiv admin note: text overlap with arXiv:1108.6319 by other author
Maximizing Happiness in Graphs of Bounded Clique-Width
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
NP-complete on threshold graphs. Hence, it is not even in XP when parameterized
by clique-width, since threshold graphs have clique-width at most two. As a
complement for this result we provide a algorithm for MHE, where is the number of colors
and is the clique-width of the input graph. We also
construct an FPT algorithm for MHV with running time
, where is the
number of colors in the input. Additionally, we show
algorithm for MHV on interval graphs.Comment: Accepted to LATIN 202
Letter Graphs and Geometric Grid Classes of Permutations: Characterization and Recognition
In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. We also present the first constructive polynomial-time algorithm for the recognition of 3-letter graphs