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Forbidden Directed Minors, Directed Path-Width and Directed Tree-Width of Tree-Like Digraphs

  • Frank Gurski
  • Carolin RehsEmail author
Conference paper
  • 425 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11376)

Abstract

There have been many attempts to find directed graph classes with bounded directed path-width and bounded directed tree-width. Right now, the only known directed tree-width-/path-width-bounded graphs are cycle-free graphs with directed path-width and directed tree-width 0. In this paper, we introduce directed versions of cactus trees and pseudotrees and -forests and characterize them by at most three forbidden directed graph minors. Furthermore, we show that directed cactus trees and forests have a directed tree-width of at most 1 and directed pseudotrees and -forests even have a directed path-width of at most 1.

Keywords

Directed cactus trees Directed pseudoforests Directed graph minors Directed path-width Directed tree-width 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Computer Science, Algorithmics for Hard Problems GroupHeinrich-Heine-University DüsseldorfDüsseldorfGermany

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