@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}
}
@article {1511,
	title = {On some applications of the selective graph coloring problem},
	journal = {European Journal of Operational Research},
	volume = {240},
	year = {2015},
	pages = {307-314},
	abstract = {<p>In this paper we present the Selective Graph Coloring Problem, a generalization of the standard graph coloring problem as well as several of its possible applications. Given a graph with a partition of its vertex set into several clusters, we want to select one vertex per cluster such that the chromatic number of the subgraph induced by the selected vertices is minimum. This problem appeared in the literature under different names for specific models and its complexity has recently been studied for different classes of graphs. Here, we describe different models {\textendash} some already discussed in previous papers and some new ones {\textendash} in very different contexts under a unified framework based on this graph problem. We point out similarities between these models, offering a new approach to solve them, and show some generic situations where the selective graph coloring problem may be used. We focus on specific graph classes motivated by each model, and we briefly discuss the complexity of the selective graph coloring problem in each one of these graph classes and point out interesting future research directions.</p>},
	keywords = {Combinatorial optimization, Computational complexity, Graph theory, partition coloring, Selective coloring},
	issn = {0377-2217},
	doi = {https://doi.org/10.1016/j.ejor.2014.05.011},
	url = {https://www.sciencedirect.com/science/article/pii/S0377221714004184},
	author = {Marc Demange and Ekim, Tinaz and Bernard Ries and Cerasela Tanasescu}
}
@article {ekim2013some,
	title = {Some Defective Parameters in Graphs},
	journal = {Graphs and Combinatorics},
	volume = {29},
	number = {2},
	year = {2013},
	pages = {213{\textendash}224},
	publisher = {Springer Japan},
	author = {Ekim, Tinaz and Gimbel, John}
}
@article {ekim2010split,
	title = {Split-critical and uniquely split-colorable graphs},
	journal = {Discrete Mathematics and Theoretical Computer Science},
	volume = {12},
	number = {5},
	year = {2010},
	pages = {1{\textendash}24},
	author = {Ekim, Tinaz and Ries, Bernard and de Werra, Dominique and others}
}
@article {ekim2006split,
	title = {On split-coloring problems (vol 10, pg 211, 2005)},
	journal = {JOURNAL OF COMBINATORIAL OPTIMIZATION},
	volume = {11},
	number = {1},
	year = {2006},
	pages = {125{\textendash}125},
	publisher = {SPRINGER VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS},
	author = {Ekim, Tinaz and de Werra, Dominique}
}
@article {ekim2005split,
	title = {On split-coloring problems},
	journal = {Journal of Combinatorial Optimization},
	volume = {10},
	number = {3},
	year = {2005},
	pages = {211{\textendash}225},
	publisher = {Kluwer Academic Publishers},
	author = {Ekim, Tinaz and de Werra, Dominique}
}
