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PRODID:-//Brown Bear Software//Calcium 4.01//EN
VERSION:2.0
METHOD:PUBLISH
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SUMMARY:On a conjecture that strengthens the $k$-factor case of Kundu's $k$-factor Theorem
UID:x-1692-Calcium@vm-mp1-int
DTSTAMP:20220517T053307Z
DTEND:20220131T190000Z
CATEGORIES:Department Seminar
ORGANIZER:MAILTO:Calcium@localhost.localdomain
DESCRIPTION:An non-negative sequence of integers $\\pi=(d_{1}\,\\ldots\,d_{n})$ is said to be\ngraphic if there exists a graph $G=(V\,E)$\, called a realization of $\\pi$\, with\n$V=\\{v_{1}\,\\ldots\, v_{n}\\}$ such that $v_{i}\\in V$ has $d_{i}$ neighbors in\n$G$. In 1974\, Kundu showed that for even $n$ if $\\pi=(d_{1}\,\\ldots\,d_{n})$ is a\nnon-increasing graphic sequence such that $(d_{1}-k\,\\ldots\,d_{n}-k)$ is graphic\,\nthen some realization of $\\pi$ has a $k$-factor. In 1978\, Brualdi and then Busch\net al.\\\, in 2012\, conjectured that not only is there a $k$-factor\, but there is\n$k$-factor that can be partitioned into $k$ edge-disjoint $1$-factors. We will\ndiscuss this conjecture and present some new supporting results.\nSpeaker: : James Shook\nAffiliation: : NIST\nLocation: :
DTSTART:20220131T180000Z
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