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Multi-compositions in Exponential Counting of Hypohamiltonian Snarks

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Convexity and Discrete Geometry Including Graph Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 148))

Abstract

An OGF and exponential asymptotic formula is found for the number of integer compositions with parts which make up a finite multiset. The novelty is that numeric parts therein can have nontrivial multiplicities. This reflects the fact that the use of distinct flip-flops of the same order in graphic compositions has enhanced the author construction of exponentially many hypohamiltonian snarks. The resulting significant improvement of lower estimates for the number of the constructed graphs will be exemplified.

Dedicated to Tudor Zamfirescu on the occasion of his 70th birthday

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Authors and Affiliations

  1. AGH Kraków, al. Mickiewicza 30, 30–059, Kraków, Poland

    Zdzisław Skupień

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  1. Zdzisław Skupień
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Correspondence to Zdzisław Skupień .

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Editors and Affiliations

  1. Einstein Institute for Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel

    Karim Adiprasito

  2. Hungarian Academy of Sciences, Rényi Institute of Mathematics, Budapest, Hungary

    Imre Bárány

  3. Mathematics of the Roumanian Academy, ``Simion Stoilow'' Institute of, Bucharest, Romania

    Costin Vilcu

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Skupień, Z. (2016). Multi-compositions in Exponential Counting of Hypohamiltonian Snarks. In: Adiprasito, K., Bárány, I., Vilcu, C. (eds) Convexity and Discrete Geometry Including Graph Theory. Springer Proceedings in Mathematics & Statistics, vol 148. Springer, Cham. https://doi.org/10.1007/978-3-319-28186-5_4

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