Abstract
In this paper, we study the upper size Ramsey number u(G1,G2)u(G1,G2), defined by Erdős and Faudree, as well as the star-critical Ramsey number r∗(G1,G2)r∗(G1,G2), defined by Hook and Isaak. We define Ramsey-full graphs and size Ramsey good graphs, and perform a detailed study on these graphs. We generalize earlier results by determining u(nKk,mKl)u(nKk,mKl) and r∗(nKk,mKl)r∗(nKk,mKl) for k,l≥3k,l≥3 and large m,nm,n; u(Cn,Cm)u(Cn,Cm) for mm odd, with n>m≥3n>m≥3; and r∗(Cn,Cm)r∗(Cn,Cm) for mm odd, with n≥m≥3n≥m≥3 and (m,n)≠(3,3)(m,n)≠(3,3).
| Original language | English |
|---|---|
| Pages (from-to) | 174-180 |
| Number of pages | 7 |
| Journal | Discrete applied mathematics |
| Volume | 202 |
| DOIs | |
| Publication status | Published - 31 Mar 2016 |
Keywords
- EWI-26837
- MSC-05C
- Upper size Ramsey number
- IR-99581
- Ramsey-full graph
- Star-critical Ramsey number
- METIS-316047
- Size Ramsey good graph
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Zhang, Y., Broersma, H. J., & Chen, Y. (2016). On star-critical and upper size Ramsey numbers. Discrete applied mathematics, 202, 174-180. https://doi.org/10.1016/j.dam.2015.08.020