Any Maximal Planar Graph with Only One Separating Triangle is Hamiltonian

Chiuyuan Chen ()
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Chiuyuan Chen: National Chiao Tung University

Journal of Combinatorial Optimization, 2003, vol. 7, issue 1, No 5, 79-86

Abstract: Abstract A graph is hamiltonian if it has a hamiltonian cycle. It is well-known that Tutte proved that any 4-connected planar graph is hamiltonian. It is also well-known that the problem of determining whether a 3-connected planar graph is hamiltonian is NP-complete. In particular, Chvátal and Wigderson had independently shown that the problem of determining whether a maximal planar graph is hamiltonian is NP-complete. A classical theorem of Whitney says that any maximal planar graph with no separating triangles is hamiltonian, where a separating triangle is a triangle whose removal separates the graph. Note that if a planar graph has separating triangles, then it can not be 4-connected and therefore Tutte's result can not be applied. In this paper, we shall prove that any maximal planar graph with only one separating triangle is still hamiltonian.

Keywords: planar graph; maximal planar graph; hamiltonian cycle; separating triangle; NP-complete (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1021998507140

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