BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hemanshu Kaul (Illinois Institute of Technology) DTSTART:20220106T050000Z DTEND:20220106T060000Z DTSTAMP:20260423T004142Z UID:ARCSIN/9 DESCRIPTION:Title: C hromatic polynomial and counting DP-colorings of graphs : Problems and pro gress\nby Hemanshu Kaul (Illinois Institute of Technology) as part of ARCSIN - Algebra\, Representations\, Combinatorics and Symmetric functions in INdia\n\n\nAbstract\nIn 1912\, Birkhoff\, introduced the chromatic po lynomial of a graph $G$ that counts the number of proper colorings of $G$. List coloring\, introduced in the 1970s by Erdos among others\, is a natu ral generalization of ordinary coloring where each vertex has a restricted list of colors available to use on it. The list color function of a graph is a list coloring analogue of the chromatic polynomial that has been stu died since 1990.\n\nDP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent ye ars after its introduction by Dvorak and Postle in 2015. Intuitively\, DP- coloring is a variation on list coloring where each vertex in the graph st ill gets a list of colors\, but identification of which colors are differe nt can change from edge to edge. It is equivalent to the question of findi ng independent transversals in a (DP-)cover of a graph. In this talk\, we will introduce a DP-coloring analogue of the chromatic polynomial called t he DP color function\, ask several fundamental open questions about it\, a nd give an overview of the progress made on them. We show that while the D P color function behaves similar to the list color function and chromatic polynomial for some graphs\, there are also some surprising fundamental di fferences. \n\nThe results are based on joint work with Jeffrey Mudrock (C LC)\, as well as several groups of students.\n LOCATION:https://researchseminars.org/talk/ARCSIN/9/ END:VEVENT END:VCALENDAR