Name
Abstract | ||
|---|---|---|
Let k be a positive integer and let F and \(H_{1}, H_{2}, \ldots , H_{k}\) be simple graphs. The proper-Ramsey number \(pr_{k}(F; H_{1}, H_{2}, \ldots , H_{k})\) is the minimum integer n such that any k-coloring of the edges of \(K_{n}\) contains either a properly colored copy of F or a copy of \(H_{i}\) in color i, for some i. We consider the case where \(F = C_{4}\) is fixed, and establish the exact value of the proper-Ramsey number when \(\{H_i\}_{i=1}^k\) is a family containing only cliques, and nearly sharp bounds for the proper-Ramsey number when \(\{H_i\}_{i=1}^k\) is a family containing only cycles or only stars. We also give a general bound for the proper-Ramsey number that is nearly tight when \(\{H_i\}_{i=1}^k\) is a family of maximal split graphs. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s00373-018-1955-z | Graphs and Combinatorics |
Keywords | Field | DocType |
Proper-Ramsey, Proper cycle, Edge-coloring forbidden colored subgraph, 05C15, 05C55 | Integer,Graph,Monochromatic color,Combinatorics,Colored,Mathematics | Journal |
Volume | Issue | ISSN |
34 | 6 | 0911-0119 |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Colton Magnant | 1 | 113 | 29.08 |
| Daniel M. Martin | 2 | 35 | 6.95 |
| Pouria Salehi Nowbandegani | 3 | 5 | 4.30 |