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Subhamiltonian toroidal graphs


The problem of determining whether a graph contains a Hamiltonian cycle is difficult but has been well-studied. A related question asks when is a graph, embeddable on a surface S, a subgraph of a Hamiltonian graph which is also embeddable on S? In particular, if a graph has genus g, is it a subgraph of a Hamiltonian graph of genus g? We answer this question for all complete graphs and complete m-partite graphs of genus 0 and 1.

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Correspondence to Thomas McKenzie.

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McKenzie, T., Overbay, S. Subhamiltonian toroidal graphs. Afr. Mat. 33, 62 (2022).

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  • Book thickness
  • Hamiltonian graphs
  • Genus

Mathematics Subject Classification

  • 05C38
  • 05C45