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Graphs and Combinatorics

, Volume 3, Issue 1, pp 1–6 | Cite as

Goodness of trees for generalized books

  • S. A. Burr
  • P. Erdös
  • R. J. Faudree
  • C. C. Rousseau
  • R. H. Schelp
  • R. J. Gould
  • M. S. Jacobson
Article

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,m1,m2,...,m t )-good.

Keywords

Large Tree Color Class Vertex Coloring Generalize Book 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • S. A. Burr
    • 1
  • P. Erdös
    • 2
  • R. J. Faudree
  • C. C. Rousseau
  • R. H. Schelp
    • 3
  • R. J. Gould
    • 4
  • M. S. Jacobson
    • 5
  1. 1.Department of Computer SciencesCity College C.U.N.Y.New YorkUSA
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary
  3. 3.Department of Mathematical SciencesMemphis State UniversityMemphisUSA
  4. 4.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  5. 5.Department of MathematicsUniversity of LouisvilleLouisvilleUSA

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