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SIGEST
SIAM Review ( IF 10.2 ) Pub Date : 2022-05-05 , DOI: 10.1137/21n975448 The Editors
SIAM Review ( IF 10.2 ) Pub Date : 2022-05-05 , DOI: 10.1137/21n975448 The Editors
SIAM Review, Volume 64, Issue 2, Page 423-423, May 2022.
The SIGEST article in this issue is Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes, by František Kardoš. The original version of this article appeared in the SIAM Journal on Discrete Mathematics in 2020. Barnette's Conjecture is a famous problem in graph theory which asserts that every cubic bipartite 3-connected planar graph has a Hamiltonian cycle. The conjecture stems from an attempt in 1880 by P. G. Tait to solve the Four Color Theorem by establishing that every cubic 3-connected planar graph has a Hamiltonian cycle. This is a stronger statement than the Four Color Theorem and it actually turns out to be false, as shown by W. T. Tutte in 1946. Barnette's Conjecture is equivalent to the statement that every plane cubic 3-connected graph with all faces of even size has a Hamiltonian cycle. Our SIGEST paper proves a closely related conjecture of Barnette and Goodey asserting that every plane cubic 3-connected graph with all faces of size at most six has a Hamiltonian cycle; this also solves an open problem from mathematical chemistry, which posited the existence of a Hamiltonian cycle under the stronger assumption that all faces have size five or six. The proof consists of several reduction steps and eventually boils the problem down to checking a finite number of configurations, which is handled with the assistance of a computer. The derivations are accompanied by high-quality graphical illustrations, and the author has provided computer code for the automated parts of the proof.
更新日期：2022-05-06
The SIGEST article in this issue is Hamiltonicity of Cubic Planar Graphs with Bounded Face Sizes, by František Kardoš. The original version of this article appeared in the SIAM Journal on Discrete Mathematics in 2020. Barnette's Conjecture is a famous problem in graph theory which asserts that every cubic bipartite 3-connected planar graph has a Hamiltonian cycle. The conjecture stems from an attempt in 1880 by P. G. Tait to solve the Four Color Theorem by establishing that every cubic 3-connected planar graph has a Hamiltonian cycle. This is a stronger statement than the Four Color Theorem and it actually turns out to be false, as shown by W. T. Tutte in 1946. Barnette's Conjecture is equivalent to the statement that every plane cubic 3-connected graph with all faces of even size has a Hamiltonian cycle. Our SIGEST paper proves a closely related conjecture of Barnette and Goodey asserting that every plane cubic 3-connected graph with all faces of size at most six has a Hamiltonian cycle; this also solves an open problem from mathematical chemistry, which posited the existence of a Hamiltonian cycle under the stronger assumption that all faces have size five or six. The proof consists of several reduction steps and eventually boils the problem down to checking a finite number of configurations, which is handled with the assistance of a computer. The derivations are accompanied by high-quality graphical illustrations, and the author has provided computer code for the automated parts of the proof.
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