Fullerene graphs have exponentially many perfect matchings

DOI10.1007/s10910-008-9471-7zbMath1196.92053arXiv0801.1438OpenAlexW1988945014WikidataQ57601462 ScholiaQ57601462MaRDI QIDQ839387

Jozef Miškuf, Jean-Sébastien Sereni, Daniel Král', František Kardoš

Publication date: 2 September 2009

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

Full work available at URL: https://arxiv.org/abs/0801.1438

zbMATH Keywords

perfect matchingfullerenefullerene graph

Mathematics Subject Classification ID

Applications of graph theory (05C90) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Connectivity (05C40)

Related Items (13)

Nice pairs of disjoint pentagons in fullerene graphs ⋮ Nice pairs of odd cycles in fullerene graphs ⋮ Shortest perfect pseudomatchings in fullerene graphs ⋮ Bipartizing fullerenes ⋮ Distance-restricted matching extendability of fullerene graphs ⋮ Long cycles in fullerene graphs ⋮ Exponentially many perfect matchings in cubic graphs ⋮ On some structural properties of generalized fullerene graphs with 13 pentagonal faces ⋮ Asymptotic enumeration of perfect matchings in \(m\)-barrel fullerene graphs ⋮ A mathematical programming model for computing the fries number of a fullerene ⋮ Three-dimensional right-angled polytopes of finite volume in the Lobachevsky space: combinatorics and constructions ⋮ Packing resonant hexagons in fullerenes ⋮ 2-resonant fullerenes

Cites Work

• Leapfrog fullerenes have many perfect matchings
• Cyclic edge-cuts in fullerene graphs
• Fullerene graphs with exponentially many perfect matchings
• Every planar map is four colorable. I: Discharging
• Every planar map is four colorable. II: Reducibility
• On lower bounds of number of perfect matchings in fullerene graphs
• The four-colour theorem
• Cyclical edge-connectivity of fullerene graphs and \((k,6)\)-cages
• New lower bound on the number of perfect matchings in fullerene graphs
• On some structural properties of fullerene graphs
• Perfect matchings in planar cubic graphs

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