Summary
This is a summary of problems and results coming out of the 20 year collaboration between Paul Erdős and authors.
Research supported by O.N.R. Grant No. N00014-91-J-1085 and N.S.A. Grant No. MDA 904-90-H-4034.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
M. Ajtai, J. Komlos and E. Szemerédi, A note on Ramsey numbers, J. Combin. Theory Ser. A 29, (1980), 354–360.
M. O. Albertson and D. M. Berman, Ramsey graphs without repeated degrees, Cong. Numer. 83 (1991), 91–96.
J. Beck, On size Ramsey numbers of paths, trees and circuits, I, J. Graph Theory 7, (1983), 115–129.
B. Bollobás, Degree multiplicities and independent sets in K 4 -free graphs, preprint.
J. A. Bondy and P. Erdős, Ramsey numbers for cycles in graphs, J. Combin. Theory Ser. B 14, (1973), 46–54.
S. A. Burr and P. Erdős, Generalizations of a Ramsey-Theoretic Result of Chvátal, J. Graph Theory 7, (1983) 39–51.
S. A. Burr, P. Erdős, R. J. Faudree, R. J. Gould, M. S. Jacobson, C. C. Rousseau, and R. H. Schelp, Goodness of trees for generalized books, Graphs Combin. 3 (1987), 1–6.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey minimal graphs for multiple copies, Proc. Koninklijke, Nederlandse Akad. Van Wetenschappen, Amsterdam, Series A. 81(2) (1978), 187–195.
S. A. Burr, P. Erdős, R. J. Faudree, and R. H. Schelp, A class of Ramsey-finite graphs, Proc. 9th S. E. Conf. on Combinatorics, Graph Theory, and Computing (1978), 171–178.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, An extremal problem in generalized Ramsey theory, Ars Combin. 10 (1980), 193–203.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey minimal graphs for the pair star - connected graph, Studia Scient. Math. Hungar. 15 (1980), 265–273.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey minimal graphs for star forests, Discrete Math. 33 (1981), 227–237.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey minimal graphs for matchings, The Theory and Applications of Graphs, G. Chartrand, editor, John Wiley (1981) 159–168.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey minimal graphs for forests, Discrete Math. 38 (1982), 23–32.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey numbers for the pair sparse graph-path or cycle, Trans. Amer. Math. Soc. 2 (269) (1982), 501–512.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, The Ramsey number for the pair complete bipartite graph - graph with limited degree, Graph Theory with Applications to Algorithms and Computer Sciences G. Chartrand, ed. Wiley-Interscience, New York, (1985), 163–174.
S. A. Burr, P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Some complete bipartite graph - tree Ramsey numbers, Ann. Discrete Math. 41 (1989), 79–90.
S. A. Burr and R. J. Faudree, On graphsGfor which all large trees areG-good, Graphs Combin. (to appear).
L. Caccetta, P. Erdős, E. T. Ordman and N. J. Pullman, The difference between the clique numbers of a graph, Ars Combin. 19A (1985), 97–106.
G. Chen, P. Erdős, C. C. Rousseau and R. H. Schelp, Ramsey problems involving degrees in edge-colored complete graphs of vertices belonging to monochromatic subgraphs, European J. Combin. 14 (1993), 183–189.
G. Chartrand and L. Lesniak, Graphs and Digraphs, Wadsworth and Brooks/Cole, Pacific Grove, California, 1986.
F. R. K. Chung and R. L. Graham, On graphs not containing prescribed induced subgraphs, A tribute to Paul Erdős, (eds. A. Baker, B. Bollobás, and A. Hajnal), Cambridge University Press, Cambridge, (1990), 111–120.
P. Erdős, Problems and results in graph theory, The Theory and Applications of Graphs, G. Chartrand, editor, John Wiley (1981) 331–341.
P. Erdős, Some recent problems and results in graph theory, combinatorics, and number theory, Proceedings 7th S-E Conf. Comb. Graph Theory, and Computing, (1976) 3–14.
P. Erdős and R. J. Faudree, Size Ramsey numbers involving matchings, Colloquia Mathematica Societatis Janos Bolyai 37 (1981), 247–264.
P. Erdős, R. J. Faudree, R. J. Gould, A. Gyárfás, and R. H. Schelp, Monochromatic coverings in colored complete graphs, Congressus Numerantium 71 (1990), 29–38.
P. Erdős, R. J. Faudree, A. Gyárfás, and R. H. Schelp, Cycles in graphs without proper subgraphs of minimal degree 3, (Proceedings of the Eleventh British Combinatorial Conference), Ars Combin. 25B (1988), 195–202.
P. Erdős, R. J. Faudree, A. Gyárfás, and R. H. Schelp, Domination in colored complete graphs, J. Graph Theory 13 (1989), 713–718.
P. Erdős, R. J. Faudree, A. Gyárfás, and R. H. Schelp, Odd cycles in graphs of given minimal degree, Graph Theory, Combinatorics, and Applications, Wiley and Sons, New York, Proceedings of the Sixth International Conference on Graph Theory and Applications, (1991), 407–418.
P. Erdős. R. J. Faudree, and E. Ordman, Clique partitions and clique coverings, Discrete Math. 72 (1988), 93–101.
P. Erdős, R. J. Faudree, T. J. Reid, R. H. Schelp, and W. Staton, Degree sequence and independence in K 4 -free graphs, to appear in Discrete Math.
P. Erdős, R. J. Faudree, and C. C. Rousseau, Extremal problems involving vertices and edges on odd cycles in graphs, Discrete Math. 101, (1992), 23–31.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Generalized Ramsey theory for multiple colors, J. of Comb. Theory B 20 (1976), 250–264.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Cycle-complete graph Ramsey numbers, J. of Graph Theory 2 (1978), 53–64.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, The Size Ramsey number, a new concept in generalized Ramsey theory, Periodica Mathematica Hungarica 9 (1978), 145–161.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey numbers for brooms, Proc. 13th S.E. Conf. on Comb., Graph Theory and Computing 283–294, (1982).
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Tree - multipartite graph Ramsey numbers, Graph Theory and Combinatorics - A Volume in Honor of Paul Erdős, Bela Bollobás, editor, Academic Press, (1984), 155–160.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Multipartite graph - sparse graph Ramsey numbers, Combinatorica 5, (1985), 311–318. (with P. Erdős, C. C. Rousseau, and R. H. Schelp.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, A Ramsey problem of Harary on graphs with prescribed size, Discrete Math. 67 (1987), 227–234.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Extremal theory and bipartite graph - tree Ramsey numbers, Discrete Math. 72 (1988), 103–112.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Book - tree Ramsey numbers, Scientia, A: Mathematics 1 (1988), 111–117.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Multipartite graph - tree Ramsey numbers, Annals of the New York Academy of Sciences, 576 (1989), 146–154, Proceedings of the First China - USA International Graph Theory Conf.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Subgraphs of minimal degree k, Discrete Math. 85, (1990), 53–58.
P. Erdős, R. J. Faudree, C. C. Rousseau, and R. H. Schelp, Ramsey size linear graphs, to appear in Proceedings of Cambridge Combinatorics Colloquium
P. Erdős, R. J. Faudree, C. C. Rousseau and R. H. Schelp, A local density condition for triangles, to appear in Discrete Math.
P. Erdős, R. J. Faudree, R. H. Schelp, and M. Simonvits An extremal result for paths, Annals of The New York Academy of Sceinces, 576 (1989), 155–162. Proceedings of the China - USA Graph Theory Conf.
P. Erdős, R. J. Faudree, and V. T. Sós, k-spectrum of a graph, to appear in Proceedings of the Seventh International Conference on Graph Theory, Combinatorics, Algorithms, and Applications, Kalamazoo, Michigan
P. Erdős and C. C. Rousseau, The size Ramsey number of a complete bipartite graph, Discrete Math. 113, (1993), 259–262.
R. J. Faudree, Ramsey minimal graphs for forests, Ars Combin., 31, (1991), 117–124.
R. J. Faudree, R. J. Gould, M. S. Jacobson, J. Lehel, and L. M. Lesniak Graph spectra, manuscript.
J. H. Kim, The Ramsey numberR(3, t) has order of magnitudet 2 ∕ logt, Random Structures and Algorithms 7 (1995), 17, 173–207.
J. Nes̆etr̆il and V. Rödl, The structure of critical graphs, Acta. Math. Acad. Sci. Hungar., 32, (1978), 295–300.
V. Nikiforov, The cycle-complete graph Ramsey numbers, Combin. Prob. and Comp. 14, (2005), 349–370.
V. Nikiforov and C. C. Rousseau, Ramsey goodness and beyond, Combinatorica 29 (2009) 227–262.
C. C. Rousseau and J. Sheehan, A class of Ramsey problems involving trees, J. London Math. Soc. (2) 18, (1978), 392–396.
J. B. Shearer, A note on the independence number of a triangle–free graph, Discrete Math. 46, (1983), 83–87.
J. Spencer, Asymptotic lower bounds for Ramsey functions, Discrete Math. 20, (1977), 69–76.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Faudree, R.J., Rousseau, C.C., Schelp, R.H. (2013). Problems in Graph Theory from Memphis. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős II. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7254-4_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7254-4_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-7253-7
Online ISBN: 978-1-4614-7254-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)