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