Induced Nets and Hamiltonicity of Claw-Free Graphs


The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net, and the vertices of degree 1 in a net are called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced \(K_{1,3}\) is hamiltonian if every endvertex of each induced net of G has degree at least \((|V(G)|-2)/3\). In this paper we prove this conjecture in the affirmative.

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Correspondence to Jun Fujisawa.

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Dedicated to Professor Katsuhiro Ota on the occasion of his 60th birthday

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Shuya Chiba: work supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) 17K05347 and 20K03720. Jun Fujisawa: work supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B) 16H03952, (C) 17K05349 and (C) 20K03723.

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Chiba, S., Fujisawa, J. Induced Nets and Hamiltonicity of Claw-Free Graphs. Graphs and Combinatorics (2021).

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  • Hamiltonian cycles
  • Claw-free graphs
  • Induced nets

Mathematics Subject Classification

  • 05C45
  • 05C38
  • 05C75