Four-terminal reducibility and projective-planar wye-delta-wye-reducible graphs

Dan Archdeacon, Charles J. Colbourn, Isidoro Gitler, J. Scott Provan

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A graph is Y ΔY-reducible if it can be reduced to a vertex by a sequence of series-parallel reductions and Y ΔY-transformations. Terminals are distinguished vertices, that cannot be deleted by reductions and transformations. In this article, we show that four-terminal planar graphs are Y ΔY-reducible when at least three of the vertices lie on the same face. Using this result, we characterize Y ΔY-reducible projective-planar graphs. We also consider terminals in projective-planar graphs, and establish that graphs of crossing-number one are Y ΔY-reducible.

Original languageEnglish (US)
Pages (from-to)83-93
Number of pages11
JournalJournal of Graph Theory
Issue number2
StatePublished - Feb 2000
Externally publishedYes


  • Reducible graphs
  • Terminal
  • Wye-delta

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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