Bounding the Clique-Width of H-free Chordal Graphs [chapter]

Andreas Brandstädt, Konrad K. Dabrowski, Shenwei Huang, Daniël Paulusma
2015 Lecture Notes in Computer Science  
Citation for published item: frndst¤ dtD eF nd hrowskiD uFuF nd rungD F nd ulusmD hF @PHISA 9founding the liqueEwidth of rEfree hordl grphsF9D in wthemtil foundtions of omputer siene PHIS X RHth snterntionl ymposiumD wpg PHISD wilnD stlyD eugust PREPVD PHISD proeedingsD prt ssF ferlinX pringerD ppF IQWEISHF veture notes in omputer sieneF @WPQSAF Further information on publisher's website: Publisher's copyright statement: The nal publication is available at Springer via http://dx.The full-text
more » ... y be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. Abstract. A graph is H-free if it has no induced subgraph isomorphic to H. Brandstädt, Engelfriet, Le and Lozin proved that the class of chordal graphs with independence number at most 3 has unbounded clique-width. Brandstädt, Le and Mosca erroneously claimed that the gem and the co-gem are the only two 1-vertex P4-extensions H for which the class of H-free chordal graphs has bounded clique-width. In fact we prove that bull-free chordal and co-chair-free chordal graphs have cliquewidth at most 3 and 4, respectively. In particular, we prove that the clique-width is: (i) bounded for four classes of H-free chordal graphs; (ii) unbounded for three subclasses of split graphs. Our main result, obtained by combining new and known results, provides a classification of all but two stubborn cases, that is, with two potential exceptions we determine all graphs H for which the class of H-free chordal graphs has bounded clique-width. We illustrate the usefulness of this classification for classifying other types of graph classes by proving that the class of (2P1 + P3, K4)-free graphs has bounded clique-width via a reduction to K4-free chordal graphs. Finally, we give a complete classification of the (un)boundedness of clique-width of H-free weakly chordal graphs.
doi:10.1007/978-3-662-48054-0_12 fatcat:74newl3elzetxe2kg5rx5bzooe