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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 張鎮華(Gerard Jennhwa Chang) | |
dc.contributor.author | Yen-Jen Cheng | en |
dc.contributor.author | 鄭硯仁 | zh_TW |
dc.date.accessioned | 2021-05-20T21:45:12Z | - |
dc.date.available | 2010-08-09 | |
dc.date.available | 2021-05-20T21:45:12Z | - |
dc.date.copyright | 2010-08-09 | |
dc.date.issued | 2010 | |
dc.date.submitted | 2010-08-06 | |
dc.identifier.citation | [1] J. Beck, On size Ramsey number of paths, trees and cycles I, J. Graph Theory 7 (1983), 115-30.
[2] J. Beck, On size Ramsey number of paths, trees and cycles II, Mathematics of Ramsey Theory (Springer), Algorithms and Combin. 5 (1990), 34-5. [3] M. Borowiecki, M. Haluszczac and E. Sidorowicz, On Ramsey minimal graphs, Discrete Math. 286 (2004), 37-43. [4] S. A. Burr, P. Erdos, R. J. Faudree, C. C. Rousseau and R. H. Schelp, Ramseyminimal graphs for multiple copies, Nederl. Akad. Wetensch. Indag. Math. 40 (1978), 187-195. [5] S. A. Burr, P. Erdos, R. J. Faudree, C. C. Rousseau and R. H. Schelp, Ramseyminimal graphs for star-forest, Discrete Math. 33 (1981), 227-237. [6] S. A. Burr, P. Erdos, and L. Lovasz, On graphs of Ramsey type, Ars Combinatoria 1 (1976), 167-190. [7] J. Buttereld, T. Grauman, B. Kinnersley, K.G. Milans, C. Stocker and D. B. West, On-line Ramsey Theory for bounded degree graphs, submitted. [8] G. Chartrand and L. Lesniak, Graphs and Digraphs, Chapman HALL/CRC, 2005 [9] J. Donadelli, P.E. Haxell and Y. Kohayakawa, A note on the size-Ramsey number of long subdivisions of graphs, RAIRO-Inf. Theor. Appl. 39 (2005), 191-206. [10] P. Erdos, R. J. Faudree, C. C. Rousseau and R. H. Schelp, The size Ramsey number, Periodic Math. Hung. 9 (1978), 145-161. [11] J. Folkman, Graphs with monochromatic complete subgraphs in every edge coloring, SIAM J. Appl. Math. 18 (1970), 19-24. [12] Z. K. Min, A note on the size Ramsey number for stars, JAMCC. 11 (1992), 209- 212. [13] J. Nesetril and V. Rodl, Type theory of partition properties of graphs, in: Recent Advances in Graph Theory, Proc. Second Czechoslovak Sympos., Prague, 1974, Academia, Prague (1975), 405-412. [14] V. Rodl and E. Szemeredi, On size Ramsey numbers of graphs with bounded maximum degree, Combinatorica 20 (2000), 257-262. [15] D. B. West, Introduction to Graph Theory, Prentice-Hall, Upper Saddle River, NJ (1996). [16] X. Zhu, Chromatic Ramsey numbers. Discrete Math. 190 (1998), 215-222. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10630 | - |
dc.description.abstract | 對於圖 G_1, G_2, ..., G_r和 F,如果當 F的邊被著上 1, 2, ..., r這些顏色時,總是存在 i使得著顏色 i的邊中包含圖 G_$的話,則記作 F -> (G_1, G_2, ..., G_r)。在所有滿足 F -> (G_1, G_2, ..., G_r)的 F中,所含邊數的最小值稱為邊拉姆西數,記作 r(G_1, G_2, ..., G_r)。
假設 G_1 = U_{i=1}^{m}{K_{1,a_i}},G_2 = U_{i=1}^{n}{K_{1, b_i}}且 a_1 >= a_2 >= ... >= a_m,b_1 >= b_2 >= ... >= b_n,令 l_s = max_{i+j=s+1}{(a_i+b_j-1)},Burr, Erdos, Faudree, Rousseau 和 Schelp [4]猜測 $r(G_1, G_2) = sum_{s=1}^{m+n-1}{l_s}。這篇論文的目的是研究這個猜想在 a_1,b_1以外的數都等於 1時的情形。 | zh_TW |
dc.description.abstract | For graphs G_1, G_2, ..., G_r and F, we write F -> (G_1, G_2, ..., G_r)$ to mean that if the edges of
F are colored by 1, 2, ..., r then there exists some i such that the edges of color i contains a copy of G_i. The size Ramsey number r(G_1, G_2, ..., G_r) is the least number of edges of a graph F for which F -> (G_1, G_2, ..., G_r). Suppose G_1 = U_{i=1}^{m}{K_{1,a_i}} with a_1 >= a_2 >= ... >= a_m and G_2 = U_{i=1}^{n}{K_{1, b_i}} with b_1 >= b_2 >= ... >= b_n. Let l_s = max_{i+j=s+1}{(a_i+b_j-1)}. Burr, Erdos, Faudree, Rousseau and Schelp [4] conjectured that r(G_1, G_2) = sum_{s=1}^{m+n-1}{ell_s}. The purpose of this thesis is to study the conjecture for the case when a_i = b_j = 1 for 2 <= i <= m and $2 <= j <= n. | en |
dc.description.provenance | Made available in DSpace on 2021-05-20T21:45:12Z (GMT). No. of bitstreams: 1 ntu-99-R97221014-1.pdf: 780074 bytes, checksum: 68c1daf721fcbd6fe97be52bfa686d24 (MD5) Previous issue date: 2010 | en |
dc.description.tableofcontents | Acknowledgments i
Abstract (in Chinese) ii Abstract (in English) iii Contents iv 1 Introduction 1 2 Main Result 2 3 Structure of Ramsey graphs with minimum number of edges 11 Reference 14 | |
dc.language.iso | en | |
dc.title | 星星森林的邊拉姆西數 | zh_TW |
dc.title | Size Ramsey Numbers of Star Forests | en |
dc.type | Thesis | |
dc.date.schoolyear | 98-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 顏經和,葉鴻國 | |
dc.subject.keyword | 拉姆西,星星森林, | zh_TW |
dc.subject.keyword | Ramsey,star forest, | en |
dc.relation.page | 15 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2010-08-08 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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