Graph classes with and without powers of bounded cliquewidth
Abstract
We initiate the study of graph classes of powerbounded cliquewidth, that is, graph classes for which there exist integers $k$ and $\ell$ such that the $k$th powers of the graphs are of cliquewidth at most $\ell$. We give sufficient and necessary conditions for this property. As our main results, we characterize graph classes of powerbounded cliquewidth within classes defined by either one forbidden induced subgraph, or by two connected forbidden induced subgraphs. We also show that for every positive integer $k$, there exists a graph class such that the $k$th powers of graphs in the class form a class of bounded cliquewidth, while this is not the case for any smaller power.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.2135
 Bibcode:
 2014arXiv1402.2135B
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Discrete Mathematics
 EPrint:
 23 pages, 4 figures