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The Hamiltonian index of graphs
Discrete Mathematics
  • Zhi-Hong Chen, Butler University
  • Yi Hong
  • Jian-Liang Lin
  • Zhi-Sui Tao
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The Hamiltonian index of a graph GG is defined as h(G)=min{m:Lm(G) is Hamiltonian}.h(G)=min{m:Lm(G) is Hamiltonian}. In this paper, using the reduction method of Catlin [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44], we constructed a graph sourceH̃^(m)(G) from GG and prove that if h(G)≥2h(G)≥2, then h(G) = min{m : H̃^(m)(G) has a spanning Eulerian subgraph}.

This is a pre-print version of this article. The version of record is available at Elsevier.

NOTE: this version of the article is pending revision and may not reflect the changes made in the final, peer-reviewed version.

Citation Information
Zhi-Hong Chen, Yi Hong, Jian-Liang Lin and Zhi-Sui Tao. "The Hamiltonian index of graphs" Discrete Mathematics Vol. 309 Iss. 1 (2009) p. 288 - 292
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