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CATEGORIES:Combinatorics and Probability Seminar
SUMMARY:Domination in structured tournaments - Nicolas Bou
squet (CNRS\, Grenoble)
DTSTART:20170601T140000Z
DTEND:20170601T150000Z
UID:TALK2690AT
URL:/talk/index/2690
DESCRIPTION:There exists tournaments\, such as random tourname
nts\, for which the domination number is arbitrari
ly large. One can naturally ask what happens if we
add some structure on the tournament\, for instan
ce if the tournament can be represented using a bo
unded number of partial orders. Alon et al. showed
that k-majority tournaments have bounded dominati
on number. Gyarfas and Palvolgyi conjectured that
the following is true : If a tournament admits a p
artition of its arc set into k quasi orders\, then
its domination number is bounded in terms of k. W
e provide a short proof that the following more ge
neral conjecture due to Erdos\, Sands\, Sauer and
Woodrow: If the arcs of a tournament T are colored
with k colors\, there is a set X of at most g(k)
vertices such that for every vertex v of T\, there
is a monochromatic path from X to v.\n\n(joint wo
rk with William Lochet and StÃ©phan ThomassÃ©)
LOCATION:LTC Watson
CONTACT:Guillem Perarnau
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