Generalized Ramsey numbers for paths in 2-chromatic graphs
Chung and Liu have defined the d-chromatic Ramsey number as follows. Let 1≤d≤c and let t=(cd). Let 1,2,…,t be the ordered subsets of d colors chosen from c distinct colors. Let G1,G2,…,Gt be graphs. The d-chromatic Ramsey number denoted by rdc(G1,G2,…,Gt) is defined as the least number p such that,...
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000339 |
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| author | R. Meenakshi P. S. Sundararaghavan |
| author_facet | R. Meenakshi P. S. Sundararaghavan |
| author_sort | R. Meenakshi |
| collection | DOAJ |
| description | Chung and Liu have defined the d-chromatic Ramsey number as follows. Let 1≤d≤c and let t=(cd). Let 1,2,…,t be the ordered subsets of d colors chosen from c distinct colors. Let G1,G2,…,Gt be graphs. The d-chromatic Ramsey number denoted by rdc(G1,G2,…,Gt) is defined as the least number p such that, if the edges of the complete graph Kp are colored in any fashion with c colors, then for some i, the subgraph whose edges are colored in the ith subset of colors contains a Gi. In this paper it is shown that r23(Pi,Pj,Pk)=[(4k+2j+i−2)/6] where i≤j≤k<r(Pi,Pj), r23 stands for a generalized Ramsey number on a 2-colored graph and Pi is a path of order i. |
| format | Article |
| id | doaj-art-331746d9cf654dcb9fcf25602770a293 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-331746d9cf654dcb9fcf25602770a2932025-08-20T02:24:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019227327610.1155/S0161171286000339Generalized Ramsey numbers for paths in 2-chromatic graphsR. Meenakshi0P. S. Sundararaghavan1Mathematics Department, The University of Toledo, Toledo 43606, Ohio, USAComputer Systems Department, The University of Toledo, Toledo 43606, Ohio, USAChung and Liu have defined the d-chromatic Ramsey number as follows. Let 1≤d≤c and let t=(cd). Let 1,2,…,t be the ordered subsets of d colors chosen from c distinct colors. Let G1,G2,…,Gt be graphs. The d-chromatic Ramsey number denoted by rdc(G1,G2,…,Gt) is defined as the least number p such that, if the edges of the complete graph Kp are colored in any fashion with c colors, then for some i, the subgraph whose edges are colored in the ith subset of colors contains a Gi. In this paper it is shown that r23(Pi,Pj,Pk)=[(4k+2j+i−2)/6] where i≤j≤k<r(Pi,Pj), r23 stands for a generalized Ramsey number on a 2-colored graph and Pi is a path of order i.http://dx.doi.org/10.1155/S0161171286000339Ramsey numbergeneralized Ramsey numberd-chromatic Ramsey numbercolored graph. |
| spellingShingle | R. Meenakshi P. S. Sundararaghavan Generalized Ramsey numbers for paths in 2-chromatic graphs International Journal of Mathematics and Mathematical Sciences Ramsey number generalized Ramsey number d-chromatic Ramsey number colored graph. |
| title | Generalized Ramsey numbers for paths in 2-chromatic graphs |
| title_full | Generalized Ramsey numbers for paths in 2-chromatic graphs |
| title_fullStr | Generalized Ramsey numbers for paths in 2-chromatic graphs |
| title_full_unstemmed | Generalized Ramsey numbers for paths in 2-chromatic graphs |
| title_short | Generalized Ramsey numbers for paths in 2-chromatic graphs |
| title_sort | generalized ramsey numbers for paths in 2 chromatic graphs |
| topic | Ramsey number generalized Ramsey number d-chromatic Ramsey number colored graph. |
| url | http://dx.doi.org/10.1155/S0161171286000339 |
| work_keys_str_mv | AT rmeenakshi generalizedramseynumbersforpathsin2chromaticgraphs AT pssundararaghavan generalizedramseynumbersforpathsin2chromaticgraphs |