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SUMMARY:Daniel Cranston (Virginia Commonwealth University)
DTSTART:20201015T020000Z
DTEND:20201015T030000Z
DTSTAMP:20260423T021008Z
UID:SCMSComb/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SCMSComb/15/
 ">Vertex Partitions into an Independent Set and a Forest with Each Compone
 nt Small</a>\nby Daniel Cranston (Virginia Commonwealth University) as par
 t of SCMS Combinatorics Seminar\n\n\nAbstract\nFor each integer $k \\ge 2$
 \, we determine a sharp bound on\nmad(G) such that V(G) can be partitioned
  into sets I and $F_k$\, where I\nis an independent set and $G[F_k]$ is a 
 forest in which each component\nhas at most $k$ vertices. For each $k$ we 
 construct an infinite family of\nexamples showing our result is best possi
 ble. Hendrey\, Norin\, and Wood\nasked for the largest function g(a\,b) su
 ch that if mad(G) < g(a\,b)\nthen V(G) has a partition into sets A and B s
 uch that mad(G[A]) < a\nand mad(G[B]) < b. They specifically asked for the
  value of g(1\,b)\,\nwhich corresponds to the case that A is an independen
 t set.\nPreviously\, the only values known were g(1\,4/3) and g(1\,2). We 
 find\nthe value of g(1\,b) whenever 4/3 < b < 2. This is joint work with\n
 Matthew Yancey.\n\npassword 061801\n
LOCATION:https://researchseminars.org/talk/SCMSComb/15/
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