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CATEGORIES:Combinatorics and Probability seminar
SUMMARY:Antidirected subgraphs of oriented graphs - Camila
Zarate Gueren\, Birmingham
DTSTART:20230202T150000Z
DTEND:20230202T160000Z
UID:TALK5181AT
URL:/talk/index/5181
DESCRIPTION:For simple connected graphs\, minimum degree at le
ast k/2 guarantees having the k-path as a subgraph
\, if the graph has at least k+1 vertices. For ori
ented graphs\, Stein conjectured that minimum semi
degree greater than k/2 should be enough to have e
very oriented path of length k. We prove that this
is asymptotically true for large antidirected pat
hs in large graphs. Even more\, the result is true
for large antidirected trees that are balanced an
d of bounded maximum degree under the same conditi
on on the minimum semidegree. We also prove a simi
lar result for antisubdivisions of a sufficiently
small complete graph\, which implies having the k-
edge antidirected cycle.\n\nLastly\, we address a
conjecture by Addario-Berry\, Havet\, Linhares Sal
es\, Reed and Thomassé about edge density on digra
phs and antidirected trees. We show that this conj
ecture is asymptotically true for oriented graphs
with n vertices and all balanced antidirected tree
s of bounded maximum degree and of size linear in
n.\n
LOCATION:LRC
CONTACT:Dr Richard Mycroft
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