• Corpus ID: 453914

Enumeration of unlabeled graph classes

@inproceedings{Shi2016EnumerationOU,
  title={Enumeration of unlabeled graph classes},
  author={Jessica Shi and J{\'e}r{\'e}mie O. Lumbroso},
  year={2016}
}

• Jessica Shi, Jérémie O. Lumbroso
• Published 2016
• Mathematics

In this paper, we study the enumeration of certain classes of graphs that can be fully characterized by tree decompositions; these classes are particularly significant due to the algorithmic improvements derived from tree decompositions on classically NP-complete problems on these classes [12, 7, 17, 35]. Previously, Chauve et al. [6] and Iriza [26] constructed grammars from the split decomposition trees of distance hereditary graphs and 3-leaf power graphs. We extend upon these results to obtain an upper bound grammar for parity graphs. Also, Nakano et al. [25] used the vertex incremental characterization of distance hereditary graphs to obtain upper bounds. We constructively enumerate (6,2)-chordal bipartite graphs, (C5, bull, gem, co-gem)-free graphs, and parity graphs using their vertex incremental characterization and extend upon Nakano et al.’s results to analytically obtain upper bounds of O ( 7n ) and O ( 11n ) for (6,2)-chordal bipartite graphs and (C5, bull, gem, co-gem)-free graphs respectively.