Various results on the toughness of graphs

Haitze J. Broersma, E.A. Engbers, H. Trommel

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Abstract

Let G be a graph, and let t 0 be a real number. Then G is t-tough if t!(G − S) jSj for all S V (G) with !(G − S) > 1, where !(G − S) denotes the number of components of G − S. The toughness of G, denoted by (G), is the maximum value of t for which G is t-tough (taking (Kn) = 1 for all n 1). G is minimally t-tough if (G) = t and (H) < t for every proper spanning subgraph H of G. We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sucient (degree) conditions implying (G) t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversiteit Twente
Number of pages14
ISBN (Print)0169-2690
Publication statusPublished - 1997

Publication series

NameMemorandum / University of Twente, Faculty of Applied Mathematics
PublisherUniversiteit Twente
No.1372

Keywords

  • METIS-141163
  • IR-30523

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