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</head><body class="body"><span itemscope itemtype="http://schema.org/InformAction"><span style="display:none" itemprop="about" itemscope itemtype="http://schema.org/EmailMessage"><meta itemprop="description" content="Math Seminar: Theory and Computation of the Defective Ramsey Numbers"/></span><span itemprop="object" itemscope itemtype="http://schema.org/Event"><meta itemprop="eventStatus" content="http://schema.org/EventScheduled"/><span itemprop="publisher" itemscope itemtype="http://schema.org/Organization"><meta itemprop="name" content="Google Calendar"/></span><meta itemprop="eventId/googleCalendar" content="5ioh02jeckjjqlpbcq2f36a74d"/><span style="display: none; font-size: 1px; color: #fff; line-height: 1px; height: 0; max-height: 0; width: 0; max-width: 0; opacity: 0; overflow: hidden;" itemprop="name">Tınaz Ekim (Boğaziçi Üniversitesi)</span><span aria-hidden="true"><time itemprop="startDate" datetime="20241218T120000Z"></time><time itemprop="endDate" datetime="20241218T130000Z"></time></span><table border="0" cellpadding="0" cellspacing="0" role="presentation" align="center" style="width:100%;" class="body-container"><tbody><tr><td style="" class="" align="left"><!--[if mso | IE]><table border="0" cellpadding="0" cellspacing="0" role="presentation"><tr><td height="16" style="height:16px;"><![endif]--><div style="height:16px;" aria-hidden="true"> </div><!--[if mso | IE]></td></tr></table><![endif]--><table border="0" cellpadding="0" cellspacing="0" role="presentation" align="center" style="width:100%;" class=""><tbody><tr><td style="" class="" align="left"><span itemscope itemtype="http://schema.org/EmailMessage"><p itemprop="description">Theory and Computation of the Defective Ramsey Numbers</p></span></td></tr></tbody></table><table border="0" cellpadding="0" cellspacing="0" role="presentation" align="center" style="width:100%;" class=""><tbody><tr><td style="border: solid 1px #dadce0; border-radius: 8px; direction: rtl; font-size: 0; padding: 24px 32px; text-align: left; vertical-align: top;" class="main-container-inner"><!--[if mso | IE]><table border="0" cellpadding="0" cellspacing="0" role="presentation"><tr><![endif]--><div class="" style="font-size: 13px; text-align: left; direction: ltr; display: inline-block; vertical-align: top; width: 100%;overflow: hidden; word-wrap: break-word;"><table border="0" cellpadding="0" cellspacing="0" role="presentation" width="100%" class="main-column-table-ltr" style="padding-right: 32px; padding-left: 0;;table-layout: fixed;"><tbody><tr><td class="main-column-td" style="padding:0; vertical-align:top;"><table border="0" cellpadding="0" cellspacing="0" role="presentation" width="100%" style="table-layout: fixed;"><tr><td style="font-size: 0; padding: 0; text-align: left; word-break: break-word;;padding-bottom:2px;"><div style="font-family: 'Google Sans', Roboto, sans-serif;font-weight: 400; font-size: 22px; line-height: 28px;color: #3c4043; text-decoration: none;" class="primary-text" role="presentation"><span itemprop="name">Tınaz Ekim (Boğaziçi Üniversitesi)</span></div></td></tr><tr><td style="font-size: 0; padding: 0; text-align: left; word-break: break-word;;padding-bottom:24px;"><div style="font-family: Roboto, sans-serif;font-style: normal; font-weight: 400; font-size: 14px; line-height: 20px; letter-spacing: 0.2px;color: #3c4043; text-decoration: none;" class="primary-text" role="presentation"><span aria-hidden="true"><time itemprop="startDate" datetime="20241218T120000Z"></time><time itemprop="endDate" datetime="20241218T130000Z"></time></span><span>Çarşamba 18 Ara 2024 ⋅ 15:00 – 16:00 (Türkiye Saati)</span></div></td></tr><tr><td style="font-size: 0; padding: 0; text-align: left; word-break: break-word;;padding-bottom:24px;"><div style="font-family: Roboto, sans-serif;font-style: normal; font-weight: 400; font-size: 14px; line-height: 20px; letter-spacing: 0.2px;color: #3c4043; text-decoration: none;" class="primary-text" role="presentation"><span>Title: Theory and Computation of the Defective Ramsey Numbers<p>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.</p><p>T. Ekim, J. Gimbel, Some defective parameters in graphs, Graphs and Combinatorics,Volume 29, Number 2, (2013), 213-224.</p><p>Akdemir, T. Ekim, Advances on Defective Parameters in Graphs, Discrete Optimization, 16 (2015), 62-69.</p><p>T. Ekim, J. Gimbel, O. Seker, Small 1-Defective Ramsey Numbers in Perfect Graphs, Discrete Optimization, 34 (2019) 100548.</p><p>Y.E. Demirci, T. Ekim, J. Gimbel, M.A. Yildiz, Exact Values of Defective Ramsey Numbers in Graph Classes, Discrete Optimization, 42 (2021) 100673.</p><p>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</p><p>T. Ekim, B. Erdem, J. Gimbel, Sparse Sets in Triangle-free Graphs, submitted.</p><p>---</p><p>* To access to the complete seminar calendar please visit this link</p><p><a href="https://www.google.com/url?q=https%3A%2F%2Fmatematik.gsu.edu.tr%2Ftr%2Farastirma%2Fseminerler&sa=D&ust=1734528660000000&usg=AOvVaw3EDTPt9L6W0AHIJd1cJn_9" target="_blank">https://matematik.gsu.edu.tr/tr/arastirma/seminerler</a></p><p>* To add to your calendar use ical url.</p><p><a href="https://calendar.google.com/calendar/ical/mathseminar%40galatasaray.education/public/basic.ics" target="_blank">https://calendar.google.com/calendar/ical/mathseminar%40galatasaray.education/public/basic.ics</a></p><p>* Participants from outside Galatasaray Üniversitesi are kindly<br>requested to send an email to mathseminar@galatasaray.education<br>before 13:00 on the day of the seminar.</p><p>---<br>Galatasaray Üniversitesi Matematik Bölümü</p></span><meta itemprop="description" content="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.
---
* To access to the complete seminar calendar please visit this link
https://matematik.gsu.edu.tr/tr/arastirma/seminerler
* To add to your calendar use ical url.
https://calendar.google.com/calendar/ical/mathseminar%40galatasaray.education/public/basic.ics
* Participants from outside Galatasaray Üniversitesi are kindly
requested to send an email to mathseminar@galatasaray.education
before 13:00 on the day of the seminar.
---
Galatasaray Üniversitesi Matematik Bölümü"/></div></td></tr><tr><td style="font-size: 0; padding: 0; text-align: left; word-break: break-word;;padding-bottom:24px;"><div style="font-family: Roboto, sans-serif;font-style: normal; font-weight: 400; font-size: 14px; line-height: 20px; letter-spacing: 0.2px;color: #3c4043; text-decoration: none;" class="primary-text" role="presentation"><table border="0" cellpadding="0" cellspacing="0" role="presentation" style="padding-bottom: 4px;"><tr><td><h2 class="primary-text" style="font-size: 14px;color: #3c4043; text-decoration: none;font-weight: 700;-webkit-font-smoothing: antialiased;margin: 0; padding: 0;">Konum</h2></td></tr></table><span itemprop="location" itemscope itemtype="http://schema.org/Place"><span itemprop="name" class="primary-text notranslate" style="font-family: Roboto, sans-serif;font-style: normal; font-weight: 400; font-size: 14px; line-height: 20px; letter-spacing: 0.2px;color: #3c4043; text-decoration: none;">Room h306 - Galatasaray Üniversitesi, Ortaköy, Çırağan Cd. No:36, 34349 Beşiktaş/İstanbul, Türkiye</span><br/><a href="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" class="accent-text underline-on-hover" style="display: inline-block;;color: #1a73e8; text-decoration: none;font-weight: 700;" target="_blank" itemprop="map">Haritayı görüntüleyin</a></span></div></td></tr><tr><td style="font-size: 0; padding: 0; text-align: left; word-break: break-word;;padding-bottom:24px;"><div style="font-family: Roboto, sans-serif;font-style: normal; font-weight: 400; font-size: 14px; line-height: 20px; letter-spacing: 0.2px;color: #3c4043; text-decoration: none;" class="primary-text" role="presentation"><table border="0" cellpadding="0" cellspacing="0" role="presentation" style="padding-bottom: 4px;"><tr><td><h2 class="primary-text" style="font-size: 14px;color: #3c4043; text-decoration: none;font-weight: 700;-webkit-font-smoothing: antialiased;margin: 0; padding: 0;">Düzenleyen</h2></td></tr></table><div style="color: #3c4042;"><span class="notranslate"><a class="primary-text underline-on-hover" style="display: inline-block;;color: #3c4043; text-decoration: none;" href="mailto:mathseminar@galatasaray.education">Math Seminar</a></span><span itemprop="organizer" itemscope itemtype="http://schema.org/Person"><meta itemprop="name" content="Math Seminar"/><meta itemprop="email" content="mathseminar@galatasaray.education"/></span></div><div style="color: #707579;"><a class="secondary-text underline-on-hover" style="display: inline-block;;color: #70757a; text-decoration: none;" href="mailto:mathseminar@galatasaray.education">mathseminar@galatasaray.education</a></div></div></td></tr><tr><td style="font-size: 0; padding: 0; text-align: left; word-break: break-word;;padding-bottom:24px;"><div style="font-family: Roboto, sans-serif;font-style: normal; font-weight: 400; font-size: 14px; line-height: 20px; letter-spacing: 0.2px;color: #3c4043; text-decoration: none;" class="primary-text" role="presentation"><table border="0" cellpadding="0" cellspacing="0" role="presentation" style="padding-bottom: 4px;"><tr><td><h2 class="primary-text" style="font-size: 14px;color: #3c4043; text-decoration: none;font-weight: 700;-webkit-font-smoothing: antialiased;margin: 0; padding: 0;">Davetliler</h2></td></tr></table><div style="padding-bottom: 4px; text-align: left;;color: #3c4042;"></div></div></td></tr></table></td></tr></tbody></table></div><!--[if mso | IE]></tr></table><![endif]--></td></tr></tbody></table></td></tr></tbody></table></span></span></body></html>