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Saturday 9:25–9:50 112 Oelman Hall
Recycling Decycling
Chip Vandell
Indiana University-Purdue University Fort Wayne
Abstract
In this talk we will revisit the parameter ▽(G), the decycling number of a graph and look at how
it is affected when the additional constraint of independence is put on the decycling set. In particular
we will look at when decycling sets with this additional constraint exist, then find the constrained
decycling number for several classes of graphs.
Saturday 9:50–10:15 112 Oelman Hall
DNA Codewords and De Bruijn Sequences
Stephen Hartke
University of Illinois at Urbana-Champaign
Abstract
A De Bruijn sequence is a cyclic string of length n over some alphabet S such that all of the
substrings of k consecutive letters are distinct under some natural equivalence relation. Given S and
k, the motivating question is to find a maximum length De Bruijn sequence. Sixty years ago, De
Bruijn proved that a De Bruijn sequence of length |S| k exists when the equivalence relation is straight
equality.
When the alphabet is S = {A, C, G, T }, De Bruijn sequences are useful for the design and testing
of DNA codewords. Since DNA can twist back on itself, we require the k-substrings to be distinct
not only under equality but also reverse complementation. Results will be presented on the maximum
length of a De Bruijn sequence with this equivalence relation.
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