BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Søren Eilers (KU) DTSTART:20221027T141500Z DTEND:20221027T160000Z DTSTAMP:20260422T065829Z UID:CJCS/87 DESCRIPTION:Title: Ch romatic numbers for contact graphs of mutually congruent cuboids\nby S øren Eilers (KU) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\ n\nAbstract\nMotivated by a wireless channel assignment problem\, Reed & A llwright proved that there is no upper bound for the chromatic numbers of contact graphs for general cuboids in Euclidean space\, even when all corn ers fall in the integer lattice. If one dimension of the cuboids is restri cted to be 1\, the cuboids will be layered\, and consequently the four col or theorem shows that 8 colors suffice. This bound is tight by work of Bes sy\, Goncalves and Sereni.\n\nWe will study the situation when all cuboids must be mutually congruent\, with a particular interest in what happens i n cases when the rigid motion is required to preserve one or several of th e directions of the cuboids. We can provide non-trivial upper and lower bo unds for the maximally occuring chromatic numbers in many cases\, but only in a few instances we are able to determine these numbers fully. Our most satisfying result\, obtained recently with Rasmus Veber Weis Rasmussen\, is the fact that for 2x1x1 cuboids with the long side restricted to the XY plane\, the maximal chromatic number becomes exactly 5. We have only mana ged to show that 5 colors are necessary after a pointed computer search re sulting in a large cuboid structure requiring 5 colors. \n\nThis problem h as been used as a case study in a course "Experimental Mathematics” taug ht in Copenhagen for more than a decade\, and as I will detail\, much of w hat I know has been taught to me by students. My initial motivation came f rom outreach activities associated to LEGO bricks\, and I will say a few w ords about that too.\n LOCATION:https://researchseminars.org/talk/CJCS/87/ END:VEVENT END:VCALENDAR