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### Extremal theory and bipartite graph-tree Ramsey numbers

P. Erd'́os, R.J. Faudree, C.C. Rousseau, R.H. Schelp
1988 Discrete Mathematics
Also, applications of this to the determination of Ramsey number for arbitrary graphs and trees will be discussed.  ...  It will be show that if B is a bipartite graph with parts of order k and 1 (k G I), then there exists a positive constant c, such that for any tree T" of order II and for any j (0 c j c (k -l)), the Ramsey  ...  We investigate the Ramsey number r(T,, B), where T, denotes a tree on n vertices and B is a bipartite graph. Let B be a bipartite graph with parts of order k and I (k s I).  ...

### Extremal Theory and Bipartite Graph-Tree Ramsey Numbers [chapter]

P. Erdös, R.J. Faudree, C.C. Rousseau, R.H. Schelp
1988 Annals of Discrete Mathematics
Also, applications of this to the determination of Ramsey number for arbitrary graphs and trees will be discussed .  ...  It will be show that if B is a bipartite graph with parts of order k and i (k--1), then there exists a positive constant c, such that for any tree T of order n and for any j (0--j _-(k -1)), the Ramsey  ...  Erdős etal t a sparse graph    8] . It would be of interest to know which sparse graphs could replace the trees of Theorem 1 and Theorem 5 without altering the results .  ...

### Page 2010 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews
H. (1-MEMP) Some complete bipartite graph-tree Ramsey numbers. Graph theory in memory of G. A. Dirac (Sandbjerg, 1985), 79-89, Ann. Discrete Math., 41, North-Holland, Amsterdam-New York, 1989.  ...  H. (1-MEMP) Small order graph-tree Ramsey numbers. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986). Discrete Math. 72 (1988), no. 1-3, 119-127.  ...

### Bipartite Ramsey numbers involving stars, stripes and trees English

Michalis Christou, Costas S. Iliopoulos, Mirka Miller
2013 Electronic Journal of Graph Theory and Applications
We investigate the appearance of simpler monochromatic graphs such as stripes, stars and trees under a 2-colouring of the edges of a bipartite graph.  ...  Bipartite Ramsey problems deal with the same questions but the graph explored is the complete bipartite graph instead of the complete graph.  ...  Introduction Extremal graph theory problems usually ask for the max/ min order or size of a graph having certain characteristics.  ...

### Page 2542 of Mathematical Reviews Vol. , Issue 90E [page]

1990 Mathematical Reviews
(i1-MEMP) Extremal theory and bipartite graph-tree Ramsey numbers. Proceedings of the First Japan Conference on Graph Theory and Applications (Hakone, 1986).  ...  Also, applications of this to the determination of Ramsey number for arbitrary graphs and trees are discussed.” {For the entire collection see MR 89j:05007a.}  ...

### Page 64 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews
AR(n, 7,,) and EX(n are the anti-Ramsey and extremal func- tions, respectively.” 2002a:05176 05C55 Bielak, Halina (PL-MCSU-IM; Lul Gorgol, Izolda (PL-LUBT-AM; | rhe planar Ramsey number for C; and Ks  ...  In this paper we give some classes of bipartite graphs and digraphs with equal biclique cover and partition numbers.  ...

### Page 628 of Mathematical Reviews Vol. , Issue 87b [page]

1987 Mathematical Reviews
The proof is elegant and relies entirely on exterior algebra. In the second part of the paper, the author studies the following problem in extremal graph theory. Let H be a graph.  ...  2k +2) nodes (e.g., A < 1.8, if \V| < 146000).” 87b:05099 Alon, Noga (1-MIT) 87b:05100 An extremal problem for sets with applications to graph theory.  ...

### On the Ramsey number of trees versus graphs with large clique number

Ronald J. Gould, Michael S. Jacobson
1983 Journal of Graph Theory
Jacobson, M.S. and Kinch, L., "On the domination number of products of graphs II: trees", Journal of Graph Theory, Vol. 10 (1986), 97-106. 1987 22.  ...  ., Kézdy, A. and West, D., "The 2-intersection number of paths and boundeddegree trees", Journal of Graph Theory 19 (1995), 461-469. 1996 77.  ...

### Page 5874 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews
Erdés [Paul Erdés] and R. J. Faudree, Size Ramsey functions (219-238); P. Erdés [Paul Erdés], E. Gyéri and M. Simonovits, How many edges should be deleted to make a triangle-free graph bipartite?  ...  Hajnal, Decision tree complexity of COMBINATORICS 5874 Boolean functions (375-389); H. Harborth and I. Mengersen, Ram- sey numbers for graph sets with fixed numbers of edges (391-397); J.  ...

### Page 435 of Mathematical Reviews Vol. , Issue 81B [page]

1981 Mathematical Reviews
.; Joffe, Peter 81b:05080 Nearest 5 -matrices of given rank and the Ramsey problem for eigenvalues of bipartite 5 -graphs. (French summary) Problémes combinatoires et théorie des graphes (Colloq.  ...  As the extremal case, a category is said to be Ramsey if it has the A-Ramsey property for every one of its objects A.  ...

### Recent Developments in Extremal Combinatorics: Ramsey and Turán Type Problems

Benny Sudakov
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
In this paper we discuss some recent advances in this subject, focusing on two topics which played an important role in the development of extremal combinatorics: Ramsey and Turán type questions for graphs  ...  Often such problems are related to other areas including theoretical computer science, geometry, information theory, harmonic analysis and number theory.  ...  Acknowledgments I would like to thank Conlon, Fox, Keevash, Krivelevich and Markman for carefully reading this manuscript and many valuable comments, which greatly improved the presentation.  ...

### Page 6118 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews
This is the only unknown three-color Ramsey number for graphs with at most 5 edges and no isolated vertices. We also present data obtained by enumeration of all (P3, Ks —e, Ky —e) Ramsey colorings.”  ...  We also show that the bound is best possible and that the corresponding extremal graph is unique. We conclude with re- lated open problems associated with the classical extremal Turan graphs.”  ...

### Rainbow Generalizations of Ramsey Theory: A Survey

Shinya Fujita, Colton Magnant, Kenta Ozeki
2010 Graphs and Combinatorics
In this work, we collect Ramsey-type results concerning rainbow and proper edge colorings of graphs. Editions  ...  Acknowledgement The authors would like to thank Maria Axenovich, Tao Jiang and the referee for helpful comments and corrections.  ...  Bipartite Rainbow Ramsey Numbers Given two bipartite graphs G 1 and G 2 , the bipartite rainbow Ramsey number BRR(G 1 , G 2 ) is the smallest integer N such that any coloring of the edges of K N,N with  ...

### Page 2259 of Mathematical Reviews Vol. , Issue 88e [page]

1988 Mathematical Reviews
In this paper, the authors introduce the concept of Ramsey number r(®,¥) for graph sets ® and PY; obviously, it is an extension of the generalized Ramsey number r(G, H) for graphs G and H.  ...  Lebensold gave a necessary and sufficient condition for a bipartite graph to contain k edge-disjoint matchings [see J. Combin. Theory Ser. B 22 (1977), no. 3, 207-210; MR 56 #8435].  ...

### Page 1330 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews
(BR-SPL; Sado Paulo) The size-Ramsey number of trees. (English summary) Israel J. Math. 89 (1995), no. 1-3, 261-274.  ...  Summary: “Lower bounds for Ramsey numbers for hypergraphs and three colors are obtained.  ...
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