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CATEGORIES:The Archimedeans (CU Mathematical Society)
SUMMARY:Amalgamation - Dr Paul Russell (University of Camb
ridge)
DTSTART;TZID=Europe/London:20190426T190000
DTEND;TZID=Europe/London:20190426T200000
UID:TALK123646AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/123646
DESCRIPTION:Paul Erdős proved that there exist graphs with no
short cycles requiring \narbitrary many colours to
colour their vertices so that no two adjacent \nv
ertices have the same colour. Unfortunately\, the
proof does not explicitly \nconstruct such graphs.
A well known example sheet problem asks for an \n
example in the simplest case\, where we ban triang
les--cycles of length 3. \nSuch examples seem hard
to find\, and tend to contain many cycles of leng
th \n4. I shall discuss a solution to this problem
by Nesetril and Rodl using \ntheir method of "ama
lgamation" which\, while it is more complicated th
an \nother solutions\, also allows us to ban longe
r cycles (and can do much more \nbesides). No prio
r knowledge of graph theory is required.
LOCATION:MR2\, Centre for Mathematical Sciences
CONTACT:Valentin Hübner
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