Polynomial algorithms for computing the isolated toughness of interval and split graphs

Fengwei Li, Qingfang Ye, Hajo Broersma, Xiaoyan Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


The isolated toughness (Formula presented.) of a noncomplete graph G is defined as: (Formula presented.), where C(G) is the collection of all vertex cutsets of G and i(G − Y) stands for the number of isolated vertices in G − Y. If G is a complete graph, we set (Formula presented.). This isolated toughness parameter is closely related to the existence of factors and fractional factors in graphs. These factors and fractional factors are well-studied within graph theory, and have various applications in several fields related to computer science. In this article, we pay our attention to the computational complexity of computing the isolated toughness. We present polynomial algorithms for computing the exact value of (Formula presented.) for interval graphs and for split graphs, two well-studied special graph classes.

Original languageEnglish
Article numbere6345
JournalConcurrency Computation
Publication statusE-pub ahead of print/First online - 24 Apr 2021


  • factor
  • fractional factor
  • interval graph
  • isolated toughness
  • polynomial time algorithm
  • split graph


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