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Extremal theory and bipartite graph-tree Ramsey numbers

1988
*
Discrete Mathematics
*

Also, applications of this to the determination of

doi:10.1016/0012-365x(88)90198-7
fatcat:snrwr4esxreqzcuyia34yzmwky
*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). ...##
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Extremal Theory and Bipartite Graph-Tree Ramsey Numbers
[chapter]

1988
*
Annals of Discrete Mathematics
*

Also, applications of this to the determination of

doi:10.1016/s0167-5060(08)70775-1
fatcat:mggki2g7evblned5htfbq346j4
*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*[3] [4] [5] 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 . ...##
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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. ...##
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Bipartite Ramsey numbers involving stars, stripes and trees

English

2013
*
Electronic Journal of Graph Theory and Applications
*

English

We investigate the appearance of simpler monochromatic

doi:10.5614/ejgta.2013.1.2.2
fatcat:vtuybuzul5hq5jlo4kwx6ldlxe
*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. ...##
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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.} ...##
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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*. ...##
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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*. ...##
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On the Ramsey number of trees versus graphs with large clique number

1983
*
Journal of Graph Theory
*

Jacobson, M.S.

doi:10.1002/jgt.3190070109
fatcat:za52simkf5hejaztfcxladh72e
*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. ...##
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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. ...##
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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. ...##
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Recent Developments in Extremal Combinatorics: Ramsey and Turán Type Problems

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

doi:10.1142/9789814324359_0159
fatcat:6dzzmc7s3bbufe36nr3k7mh5vi
*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. ...##
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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*.” ...##
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Rainbow Generalizations of Ramsey Theory: A Survey

2010
*
Graphs and Combinatorics
*

In this work, we collect

doi:10.1007/s00373-010-0891-3
fatcat:ytvtt2g4hnhglbyx725xof43de
*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 ...##
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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]. ...##
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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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