The complexity of the Clar number problem and an exact algorithm

DOI10.1007/s10910-017-0799-8zbMath1385.92058arXiv1508.06889OpenAlexW2962995868MaRDI QIDQ1708506

Attila Bernáth, Erika R. Bérczi-Kovács

Publication date: 23 March 2018

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.06889

zbMATH Keywords

complexitygraph algorithmplanar graphfullereneClar numbercarbon nanotubes

Mathematics Subject Classification ID

Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Graph algorithms (graph-theoretic aspects) (05C85) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Complexity classes (hierarchies, relations among complexity classes, etc.) (68Q15)

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Cites Work

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• A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of \(\text C_{60}\)
• Unimodularity of the Clar number problem
• Extremal fullerene graphs with the maximum Clar number
• A min-max theorem for plane bipartite graphs
• An upper bound for the Clar number of fullerene graphs
• Face covers and the genus problem for apex graphs
• Combinatorial optimization. Polyhedra and efficiency (3 volumes)
• Alternative integer-linear-programming formulations of the Clar problem in hexagonal systems
• Sink-Stable Sets of Digraphs

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