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Subdivision Extendibility

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Abstract

Let H be a multigraph and G a graph containing a subgraph isomorphic to a subdivision of H, with S ⊂ V(G) (the ground set) the image of V(H) under the isomorphism. We consider connectivity and minimum degree or degree sum conditions sufficient to imply there is a spanning subgraph of G isomorphic to a subdivision of H on the same ground set S. These results generalize a number of theorems in the literature.

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References

  1. Bondy, J.A., Chvátal, V.: A method in graph theory, Discrete Math. 15(2), 111–135 (1976)

    Google Scholar 

  2. Brandt, S., Chen, G., Faudree, R., Gould, R.J., Lesniak, L.: Degree conditions for 2-factors, J. Graph Theory 24(2), 165–173 (1997)

    Google Scholar 

  3. Chartrand, G.,Lesniak, L.: Graphs & digraphs, 3rd edn. Chapman & Hall, London, (1996)

  4. Chen, G., Gould, R.J., Pfender, F.: New conditions for k-ordered Hamiltonian graphs, Ars Combin. 70, 245–255 (2004)

    Google Scholar 

  5. Dirac, G.A.: Some theorems on abstract graphs, Proc. London Math. Soc. 2, 69–81 (1952)

  6. Dirac, G.: Généralisations du théorème de Menger, C. R. Acad. Sci. Paris 250, 4252–4253 (1960)

  7. Egawa, Y., Faudree, R.J., Gyori, E., Ishigami, Y., Shelp, R., Hong, W.: Vertex-disjoint cycles containing specified edges, Graphs Combin. 16(1), 81–92 (2000)

    Google Scholar 

  8. Faudree, J.R., Faudree, R.J., Gould, R.J., Jacobson, M.S., Lesniak, L. On k-ordered graphs, J. Graph Theory 35(2), 69–82 (2000)

    Google Scholar 

  9. Faudree, J.R., Faudree, R.J., Gould, R.J., Jacobson, M.S., Lesniak, L., Pfender, F.: Linear forests and ordered cycles, Dis. Math. Graph Theory 24, 359–372 (2004)

    Google Scholar 

  10. Faudree, R.J.: Survey of reslts on k-ordered graphs, Discrete Math. 229(1–3), 73–87 (2001)

    Google Scholar 

  11. Ferrara, M., Gould, R., Tansey, G., Whalen, T.: On H-linked graphs, Graphs Combin. 11(2), 217–224 (2006)

    Google Scholar 

  12. Gould, R., Whalen, T.: Distance between two k-sets and path-systems extendibility, Ars Combin. 79, 211–228 (2006)

    Google Scholar 

  13. Justesen, P.: On independent circuits in finite graphs and a conjecture of Erdős and Pósa, Graph theory in memory of G. A. Dirac (Sandbjerg, 1985), Ann. Discrete Math. 41, 299–305 (1989)

  14. Ng, L., Schultz, M.: k-ordered Hamiltonian graphs, J. Graph Theory 24(1), 45–57 (1997)

    Google Scholar 

  15. Ore, O.: Note on Hamilton circuits, Amer. Math. Monthly 67, 55–55 (1960)

    Google Scholar 

  16. Ore, O.: Hamiltonian connected graphs, J. Math. Pures Appl. 42, 21–27 (1963)

    Google Scholar 

  17. Whitney, H.: Non-separable and planar graphs, Trans. Amer. Math. Soc. 34(2), 339–362 (1932)

    Google Scholar 

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Authors and Affiliations

  1. Emory University, Atlanta, GA, 30322, USA

    Ronald Gould

  2. Consultant, Atlanta, GA, USA

    Thor Whalen

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  1. Ronald Gould
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  2. Thor Whalen
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Correspondence to Thor Whalen.

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Gould, R., Whalen, T. Subdivision Extendibility. Graphs and Combinatorics 23, 165–182 (2007). https://doi.org/10.1007/s00373-006-0665-0

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  • DOI: https://doi.org/10.1007/s00373-006-0665-0

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