New Graph Classes of Bounded Clique-Width

Andreas Brandstädt, Feodor F. Dragan, Hoàng-Oanh Le, Raffaele Mosca
2004 Theory of Computing Systems  
Clique-width of graphs is a major new concept with respect to efficiency of graph algorithms; it is known that every algorithmic problem expressible in a certain kind of Monadic Second Order Logic called LinEMSOL(τ1,L) by Courcelle, Makowsky and Rotics, is solvable in linear time on any graph class with bounded clique-width for which a k-expression for the input graph can be constructed in linear time. The concept of clique-width extends the one of treewidth since bounded treewidth implies
more » ... ed clique-width. We give a complete classification of all graph classes defined by forbidden one-vertex extensions of the P4 with respect to their clique-width. Our results extend and improve recently published structural and complexity results in a systematic way.
doi:10.1007/s00224-004-1154-6 fatcat:a3yucbewjvgejikclpwtxnym3y