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UID:9a56937f4492c6755205ef72dcf53bc4
CATEGORIES:Discrete Math
CREATED:20231117T083309
SUMMARY: The H-space of a random graph
LOCATION:Hill 705
DESCRIPTION:Abstract:  The edge space of a graph G is the vector space of functions fro
 m E(G) to F_2 (the two-element field) with members naturally identified wit
 h subgraphs of G, and the H-space is the subspace spanned by copies of the 
 graph H. We are interested in understanding when the random graph is likely
  to have the most generic possible H-space. For example, if H is a triangle
 , we want to know when it is likely that every cycle is in the H-space (i.e
 . when the triangle space is likely the same as the cycle space). We give a
 n essentially complete answer for strictly 2-balanced graphs, showing that 
 a simple necessary condition in fact characterizes when the H-space is as g
 eneric as possible. Joint with Jeff Kahn.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract</strong>:&nbsp;&nbsp;The edge space of a graph G is the
  vector space of functions from E(G) to F_2 (the two-element field) with me
 mbers naturally identified with subgraphs of G, and the H-space is the subs
 pace spanned by copies of the graph H. We are interested in understanding w
 hen the random graph is likely to have the most generic possible H-space. F
 or example, if H is a triangle, we want to know when it is likely that ever
 y cycle is in the H-space (i.e. when the triangle space is likely the same 
 as the cycle space). We give an essentially complete answer for strictly 2-
 balanced graphs, showing that a simple necessary condition in fact characte
 rizes when the H-space is as generic as possible. Joint with Jeff Kahn.</p>
CONTACT:Speaker: Quentin Dubroff
DTSTAMP:20260828T184545
DTSTART;TZID=America/New_York:20231120T140000
DTEND;TZID=America/New_York:20231120T150000
SEQUENCE:0
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