[Turkmath:6861] Tınaz Ekim (Boğaziçi Üniversitesi)

[Math Seminar]

Theory and Computation of the Defective Ramsey Numbers

Tınaz Ekim (Boğaziçi Üniversitesi)
Çarşamba 18 Ara 2024 ⋅ 15:00 – 16:00
Türkiye Saati

Konum
Room h306 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349  
Beşiktaş/İstanbul, Türkiye	
https://www.google.com/maps/search/Room+h306+-+Galatasaray+%C3%9Cniversitesi,+Ortak%C3%B6y,+%C3%87%C4%B1ra%C4%9Fan+Cd.+No:36,+34349+Be%C5%9Fikta%C5%9F%2F%C4%B0stanbul,+T%C3%BCrkiye?hl=tr



Title: Theory and Computation of the Defective Ramsey Numbers

Abstract: We investigate a variant of Ramsey numbers called defective  
Ramsey numbers, introduced by Ekim and Gimbel in 2013, where cliques and  
independent sets are generalized to k-dense and k-sparse sets, both  
commonly called k-defective sets. Following some defective parameters in  
general graphs, we focus on the computation of defective Ramsey numbers in  
some restricted graph classes: cographs, chordal graphs, bipartite graphs,  
perfect graphs, split graphs, cacti, and triangle-free graphs. We adopt a  
two-fold approach to tackle defective Ramsey numbers. We provide direct  
proofs using structural graph theory. When this technique falls short in  
obtaining new values of defective Ramsey numbers, we use efficient graph  
enumeration techniques for structured graphs.

T. Ekim, J. Gimbel, Some defective parameters in graphs, Graphs and  
Combinatorics,Volume 29, Number 2, (2013), 213-224.

Akdemir, T. Ekim, Advances on Defective Parameters in Graphs, Discrete  
Optimization, 16 (2015), 62-69.

T. Ekim, J. Gimbel, O. Seker, Small 1-Defective Ramsey Numbers in Perfect  
Graphs, Discrete Optimization, 34 (2019) 100548.

Y.E. Demirci, T. Ekim, J. Gimbel, M.A. Yildiz, Exact Values of Defective  
Ramsey Numbers in Graph Classes, Discrete Optimization, 42 (2021) 100673.

Y.E. Demirci, T. Ekim, M.A. Yildiz, Defective Ramsey Numbers and Defective  
Cocolorings in Some Subclasses of Perfect Graphs, Graphs and Combinatorics,  
(2023) 39:18

T. Ekim, B. Erdem, J. Gimbel, Sparse Sets in Triangle-free Graphs,  
submitted.

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* Participants from outside Galatasaray Üniversitesi are kindly
requested to send an email to mathseminar at galatasaray.education
before 13:00 on the day of the seminar.

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Galatasaray Üniversitesi Matematik Bölümü

Düzenleyen
Math Seminar
mathseminar at galatasaray.education

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