### Abstract

We study several P-complete graph problems and show that they are in NC if the input graphs are restricted to be tree-structured. These graphs are also known as partial k-trees, decomposable graphs or graphs of bounded tree width, and include outerplanar graphs, series-parallel graphs and Halin graphs. The particular problems investigated herein include the lexicographically first (l.f.) depth-first search tree and the l.f. maximal independent set. It is also shown that if a tree of faces of an outerplanar graph is given, then its dfs tree can be found in O(log_{2}n) time using O(n/log_{2}n) processors.

Original language | English (US) |
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Title of host publication | Mathematical Foundations of Computer Science 1989, Proceedings |

Editors | Antoni Kreczmar, Grazyna Mirkowska |

Publisher | Springer Verlag |

Pages | 185-195 |

Number of pages | 11 |

ISBN (Print) | 9783540514862 |

DOIs | |

State | Published - Jan 1 1989 |

Externally published | Yes |

Event | 14th Symposium on Mathematical Foundations of Computer Science, MFCS 1989 - Porabka-Kozubnik, Poland Duration: Aug 28 1989 → Sep 1 1989 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 379 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 14th Symposium on Mathematical Foundations of Computer Science, MFCS 1989 |
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Country | Poland |

City | Porabka-Kozubnik |

Period | 8/28/89 → 9/1/89 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Mathematical Foundations of Computer Science 1989, Proceedings*(pp. 185-195). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 379 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-51486-4_66