Each maximal planar graph with exactly two separating triangles is Hamiltonian

Authors:
Guido Helden
Affiliations:
Department of Mathematics-C, RWTH Aachen University, 52056 Aachen, Germany
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 1
Cited 1

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GD'12 Proceedings of the 20th international conference on Graph Drawing

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Abstract

A classical result of Whitney states that each maximal planar graph without separating triangles is Hamiltonian, where a separating triangle is a triangle whose removal separates the graph. Chen [Any maximal planar graph with only one separating triangle is Hamiltonian J. Combin. Optim. 7 (2003) 79-86] proved that any maximal planar graph with only one separating triangle is still Hamiltonian. In this paper, it is shown that the conclusion of Whitney's Theorem still holds if there are exactly two separating triangles.