Closure and forbidden pairs for Hamiltonicity

  • Authors:

  • Zdenek Ryjácek

  • Affiliations:

  • Department of Mathematics, University of West Bohemia and Institute of Theoretical Computer Science (ITI), Charles University, Pilsen 306 14, Czech Republic

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2002

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Abstract

Let C be the claw K1,3 and N the net, i.e. the only connected graph with degree sequence 333111. It is known (Bedrossian, Thesis, Memphis State University, USA, 1991; Faudree and Gould, Discrete Math. 173 (1997), 45-60) that if X, Y is a pair of connected graphs, then, for any 2-connected graph G, G being XY-free implies G is hamiltonian if and only if X is the claw C and Y belongs to a finite list of graphs, one of them being the net N. For any such pair X, Y we show that the closures of all 2- connected XY-free graphs form a subclass of the class of CN-free graphs, and we fully describe their structure.