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UID:www.tcs.tifr.res.in/event/1483
DTSTAMP:20241003T111358Z
SUMMARY:Flexible list colorings
DESCRIPTION:Speaker: Rogers Mathew (IIT Hyderabad)\n\nAbstract: \nIn classi
 cal vertex coloring we wish to color the vertices of a graph G with up to 
 m colors from [m] so that adjacent vertices receive different colors\, a s
 o-called 'proper m-coloring'. List coloring is a well-known variation of c
 lassical vertex coloring that was introduced independently by Vizing and E
 rdos\, Rubin\, and Taylor in the 1970s. For list coloring\, we associate a
  'list assignment' L with a graph G such that each vertex v in G is assign
 ed a list of colors L(v) (we say L is a list assignment for G). An 'L-colo
 ring' of G is a function f with domain V(G) such that f(v) is a member of 
 L(v) for every vertex v in G. We say that G is 'L-colorable' if there exis
 ts a proper L-coloring of G: an L-coloring where adjacent vertices receive
  different colors. A list assignment L for G is called a 'k-assignment' if
  |L(v)|=k for each vertex v in G. We say G is 'k-choosable' or 'k-list col
 orable' if G is L-colorable whenever L is a k-assignment for G. The 'list 
 chromatic number' of G is the smallest k such that G is k-choosable.  \n
  \nFlexible list coloring was introduced by [Dvorak\, Norin\, and Postle
 \, 2019] in order to address a situation in list coloring where we still s
 eek a proper list coloring\, but a preferred color is given for some subse
 t of vertices and we wish to color as many vertices in this subset with it
 s preferred colored as possible\, a flexible version of the classical pr
 ecoloring extension problem. In this talk\, we explore the notion of flexi
 ble list colorings. We describe easy-to-follow proofs of two general resu
 lts and pose several open questions. \n \nThis talk is based on a joint 
 work with Hemanshu Kaul\, Jeffrey Mudrock\, and Michael Pelsmajer. \n \n
 Short Bio: Rogers Mathew is an associate professor in the Department of Co
 mputer Science and Engineering\, IIT Hyderabad. He works in graphs theory\
 , combinatorics\, and graph algorithms. \n
URL:https://www.tcs.tifr.res.in/web/events/1483
DTSTART;TZID=Asia/Kolkata:20241015T160000
DTEND;TZID=Asia/Kolkata:20241015T173000
LOCATION:A-201 (STCS Seminar Room)
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