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Goodness of trees for generalized books

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Abstract

A connected graphG is said to beF-good if the Ramsey numberr(F, G) is equal to(x(F) − 1)(p(G) − 1) + s(F), wheres(F) is the minimum number of vertices in some color class under all vertex colorings by χ (F) colors. It is of interest to know which graphsF have the property that all trees areF-good. It is shown that any large tree isK(1, 1,m 1,m 2,...,m t )-good.

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References

  1. Behzad, M., Chartrand, G., Lesniak-Foster, L.: Graphs & Digraphs. Belmont, CA: Wadsworth 1979

  2. Burr, S.A., Erdös, P., Faudree, R.J., Rousseau, C.C., Schelp, R.H.: Ramsey numbers for the pair sparse graph path or cycle. Trans. Amer. Math. Soc.269, 501–512 (1982)

    Google Scholar 

  3. Burr, S.A., Erdös, P., Faudree, R.J., Rousseau, C.C., Schelp, R.H.: Some complete bipartite graphs—tree Ramsey numbers. Proc. First Danish Intl. Conf. on Graph Theory (to appear)

  4. Burr, S.A., Faudree, R.J., Rousseau, C.C., Schelp, R.H.: On Ramsey numbers involving starlike multipartite graphs. J. Graph Theory7, 395–409 (1983)

    Google Scholar 

  5. Chvátal, V.: Tree-complete graph Ramsey numbers. J. Graph Theory1, 93 (1977)

    Google Scholar 

  6. Erdös, P., Faudree, R.J., Rousseau, C.C., Schelp, R.H.: Multipartite graph-sparse graph Ramsey numbers Combinatorica5, 311–318 (1985)

    Google Scholar 

  7. Hall, P.: On representatives of subsets, J. London Math. Soc.10, 26–30 (1935)

    Google Scholar 

  8. Harary, F.: Graph Theory. Reading, MA: Addison-Wesley 1969

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Sciences, City College C.U.N.Y., 10031, New York, NY, USA

    S. A. Burr

  2. Mathematical Institute of the Hungarian Academy of Sciences, H-1053, Budapest, Hungary

    P. Erdös

  3. Department of Mathematical Sciences, Memphis State University, 38152, Memphis, TN, USA

    R. H. Schelp

  4. Department of Mathematics and Computer Science, Emory University, 30322, Atlanta, GA, USA

    R. J. Gould

  5. Department of Mathematics, University of Louisville, 40292, Louisville, KY, USA

    M. S. Jacobson

Authors
  1. S. A. Burr
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  2. P. Erdös
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  3. R. J. Faudree
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  4. C. C. Rousseau
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  5. R. H. Schelp
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  6. R. J. Gould
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  7. M. S. Jacobson
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Additional information

The work on this manuscript was done when the seven authors met at Memphis State University to celebrate the seventy-first birthday of Paul Erdös.

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Burr, S.A., Erdös, P., Faudree, R.J. et al. Goodness of trees for generalized books. Graphs and Combinatorics 3, 1–6 (1987). https://doi.org/10.1007/BF01788524

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  • DOI: https://doi.org/10.1007/BF01788524

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