@article {1500, title = {Small 1-defective Ramsey numbers in perfect graphs}, journal = {Discrete Optimization}, volume = {34}, year = {2019}, pages = {100548}, abstract = {

In this paper, we initiate the study of defective Ramsey numbers for the class of perfect graphs. Let PG be the class of all perfect graphs and R1PG(i,j) denote the smallest n such that all perfect graphs on n vertices have either a 1-dense i-set or a 1-sparse j-set. We show that R1PG(3,j)=j for any j>=2, R1PG(4,4)=6, R1PG(4,5)=8, R1PG(4,6)=10, R1PG(4,7)=13, R1PG(4,8)=15 and R1PG(5,5)=13. We exhibit all extremal graphs for R1PG(4,7)=13 (there are exactly three). We also obtain the 1-defective Ramsey number of order (4,7) in triangle-free perfect graphs, namely R1ΔPG(4,7)=12.

}, keywords = {-dense, -dependent, -sparse, Extremal graphs}, issn = {1572-5286}, doi = {https://doi.org/10.1016/j.disopt.2019.06.001}, url = {https://www.sciencedirect.com/science/article/pii/S1572528618301622}, author = {Ekim, Tinaz and John Gimbel and Oylum {\c S}eker} }