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Hamiltonicity in k-tree-Halin Graphs

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Convexity and Discrete Geometry Including Graph Theory

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

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Abstract

A k -tree-Halin graph is a planar graph \(F\cup C\), where F is a forest with at most k components and C is a cycle, such that V(C) is the set of all leaves of F, C bounds a face and no vertex has degree 2. This is a generalization of Halin graphs. We are investigating here the hamiltonicity and traceability of k-tree-Halin graphs.

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Acknowledgments

Thanks are due to the referees of this paper. The second author’s work was supported by a grant of the Roumanian National Authority for Scientific Research, CNCS—UEFISCDI, project number PN-II-ID-PCE-2011-3-0533.

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Authors and Affiliations

  1. Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan

    Ayesha Shabbir

  2. Faculty of Mathematics, University of Dortmund, 44221, Dortmund, Germany

    Tudor Zamfirescu

  3. “Simion Stoilow” Institute of Mathematics, Roumanian Academy, Bucharest, Roumanian

    Tudor Zamfirescu

Authors
  1. Ayesha Shabbir
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  2. Tudor Zamfirescu
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Corresponding author

Correspondence to Tudor Zamfirescu .

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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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Shabbir, A., Zamfirescu, T. (2016). Hamiltonicity in k-tree-Halin Graphs. 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_5

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