Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  672.05063
Autor:  Burr, Stefan A.; Erdös, Paul; Faudree, Ralph J.; Rousseau, C.C.; Schelp, R.H.
Title:  Some complete bipartite graph-tree Ramsey numbers. (In English)
Source:  Graph theory in memory of G. A. Dirac, Pap. Meet., Sandbjerg/Den. 1985, Ann. Discrete Math. 41, 79-89 (1989).
Review:  [For the entire collection see Zbl 656.00008.]
For graphs G and H, the Ramsey number r(G,H) is the smallest positive integer n so that every 2-coloring of the edges of Kn, the complete graph on n vertices, contains either a copy of G with all of its edges colored with the first color of a copy of H with all of its edges colored with the second color. The authors prove:
For any tree T on n vertices with maximum degree m,

r(K2,2,T) = max {4,n+1,r(K2,2,K1,m)};

r(K3,3,T) \leq max {n+[cn1/3],r(K3,3,K1,m)},

for some constant c, and, except for the choice of c, this is best possible.
Reviewer:  J.E.Graver
Classif.:  * 05C55 Generalized Ramsey theory
Keywords:  Ramsey number
Citations:  Zbl 656.00008

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