Ramsey numbers for the pair sparse graphpath or cycle
Authors:
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau and R. H. Schelp
Journal:
Trans. Amer. Math. Soc. 269 (1982), 501512
MSC:
Primary 05C55
MathSciNet review:
637704
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Abstract: Let be a connected graph on vertices with no more than edges, and or a path or cycle with vertices. In this paper we will show that if is sufficiently large and is sufficiently small then for odd Also, for , where is the independence number of an appropriate subgraph of and is 0 or depending upon , and .
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 J. A. Bondy and P. Erdös, Ramsey numbers for cycles in graphs, J. Combin. Theory Ser. B 14 (1973), 4654. MR 0317991 (47:6540)
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 S. A. Burr, Generalized Ramsey theory for graphsa survey, Graphs and Combinatorics, Lecture Notes in Math., vol. 406, SpringerVerlag, Berlin and New York, 1974, pp. 5275. MR 0379210 (52:116)
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 , Ramsey numbers involving graphs with long suspended paths, J. London Math. Soc. (to appear).
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 V. Chvátal, Treecomplete graph Ramsey numbers, J. Graph Theory 1 (1977), 93. MR 0465920 (57:5806)
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 R. J. Faudree, S. L. Lawrence, T. D. Parsons and R. H. Schelp, Pathcycle Ramsey numbers, Discrete Math. 10 (1974), 269277. MR 0357195 (50:9663)
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 L. Gerencsér and A. Gyárfas, On Ramseytype problems, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 10 (1967), 6770. MR 0239997 (39:1351)
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 P. Hall, On representatives of subsets, J. London Math. Soc. 10 (1935), 2630.
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 F. Harary, Graph theory, AddisonWesley, Reading, Mass., 1969. MR 0256911 (41:1566)
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 T. D. Parsons, Pathstar Ramsey numbers, J. Combin. Theory Ser. B 17 (1974), 5158. MR 0382069 (52:2957)
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DOI:
http://dx.doi.org/10.1090/S00029947198206377045
PII:
S 00029947(1982)06377045
Article copyright:
© Copyright 1982
American Mathematical Society
