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4
votes
1answer
106 views

Example of $MSO_2$ definable NP-hard problem on bounded clique-width graphs

All $MSO_1$ and $MSO_2$ definable graph problems can be solved in linear time on bounded tree-width graphs by Courcelle's theorem. But it seems this theorem doesn't work for $MSO_2$ definable graph ...
17
votes
0answers
186 views

Courcelle's theorem for bounded clique-width graphs

Courcelle's theorem states that "Every graph property which is expressible in monadic second order logic is decidable in linear time for bounded tree-width graphs". Later it was extended to bounded ...
0
votes
0answers
52 views

Number of k-expressions of graph (clique Width)

The clique-width of a graph $G$ is the minimum number of labels needed to construct G by means of the following 4 operations. The Construction of a graph $G$ using the four operations is represented ...
12
votes
1answer
108 views

Clique-width expressions with logarithmic depth

When we are given a tree decomposition of a graph $G$ with width $w$, there are several ways in which we can make it "nice". In particular, it is known that it is possible to transform it into a tree ...
14
votes
1answer
512 views

Modular Decomposition and Clique-width

I am trying to understand some concepts about Modular decomposition and Clique-width graphs. In this paper ("On P4-tidy graphs"), there is a proof of how to solve optimization problems like ...
10
votes
2answers
344 views

MSOL optimization problems on graphs of bounded cliquewidth, with cardinality predicates

CMSOL is Counting Monadic Second Order Logic, i.e. a logic of graphs where the domain is the set of vertices and edges, there are predicates for vertex-vertex adjacency and edge-vertex incidence, ...
13
votes
2answers
511 views

Is clique-width preserved under edge contractions?

Let $G$ be class of graphs with bounded clique-width. In each graph in $G$ some edges are contracted (e.g. randomly). Is now the clique-width still bounded? In case it is (in general) no longer ...
23
votes
1answer
320 views

Cliquewidth of Almost Cographs

(I posted this question to MathOverflow two weeks ago, but so far without a rigorous answer) I have a question about graph width measures of undirected simple graphs. It is well-known that cographs ...