Clique-Width for Hereditary Graph Classes [article]

Konrad K. Dabrowski, Matthew Johnson, Daniël Paulusma
2019 arXiv   pre-print
Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class G is bounded by a constant, a wide range of problems that are NP-complete in general can be shown to be polynomial-time solvable on G. For this reason, the boundedness or unboundedness of clique-width has been investigated and determined for many graph classes. We survey these results for hereditary graph classes, which are the graph classes closed
more » ... taking induced subgraphs. We then discuss the algorithmic consequences of these results, in particular for the Colouring and Graph Isomorphism problems. We also explain a possible strong connection between results on boundedness of clique-width and on well-quasi-orderability by the induced subgraph relation for hereditary graph classes.
arXiv:1901.00335v2 fatcat:3mb44qloc5cxxddyimwo6horqa