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

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


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.


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


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© 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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