Monday, January 31, 2022 11am to 12pm
About this Event
1201 Larimer Street
Dept. of Mathematical and Statistical Sciences Fall 2021 Seminar Series Presents
Dr. James Shook
Security Components and Mechanisms Group, NIST
WHEN: Monday January 31st, 2022, from 11:00am to noon
TITLE: On a conjecture that strengthens the $k$-factor case of Kundu's $k$-factor Theorem
ABSTRACT: An non-negative sequence of integers $\pi=(d_{1},\ldots,d_{n})$ is said to be
graphic if there exists a graph $G=(V,E)$, called a realization of $\pi$, with
$V=\{v_{1},\ldots, v_{n}\}$ such that $v_{i}\in V$ has $d_{i}$ neighbors in
$G$. In 1974, Kundu showed that for even $n$ if $\pi=(d_{1},\ldots,d_{n})$ is a
non-increasing graphic sequence such that $(d_{1}-k,\ldots,d_{n}-k)$ is graphic,
then some realization of $\pi$ has a $k$-factor. In 1978, Brualdi and then Busch
et al.\, in 2012, conjectured that not only is there a $k$-factor, but there is
$k$-factor that can be partitioned into $k$ edge-disjoint $1$-factors. We will
discuss this conjecture and present some new supporting results.
Everyone is welcome to join the seminar. Seminar will be hydrid: in-person and virtual (zoom). The speaker will be remote. For in-person, please join us in Student Commons Building room #4017. For virtual attendance, please contact mathstaff@ucdenver.edu for Zoom information.