A note on degree conditions for Hamiltonicity in 2-connected claw-free graphs

  • Authors:

  • Ondrej Kovárík;Milos Mulac;Zdenek Ryjácek

  • Affiliations:

  • Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzen, Czech Republic;Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzen, Czech Republic;Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzen, Czech Republic

  • Venue:
  • Discrete Mathematics - Algebraic and topological methods in graph theory
  • Year:
  • 2002

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Abstract

Let G be a claw-free graph and let cl(G) be the closure of G. We present a method for characterizing classes Gi, i = 3,..., 7, of 2-connected closed claw-free graphs with the following properties. (i) Theorem. Let G be a 2-connected claw-free graph of order n ≥ 153 such that δ(G) ≥ 20 and σ8(G) n + 39. Then either G is hamiltonian or cl (G) ∈ ∪i=37 Gi. (ii) Corollary. Let G be a 2-connected claw-free graph of order n ≥ 153 with δ(G) ≥ (n + 39)/8. Then either G is hamiltonian or cl (G) ∈ ∪i=37 Gi.The family of exceptions contains 318 infinite classes. The majority of these exception classes were found with the help of a computer.