37 research outputs found
An extensive English language bibliography on graph theory and its applications, supplement 1
Graph theory and its applications - bibliography, supplement
The Interlace Polynomial
In this paper, we survey results regarding the interlace polynomial of a
graph, connections to such graph polynomials as the Martin and Tutte
polynomials, and generalizations to the realms of isotropic systems and
delta-matroids.Comment: 18 pages, 5 figures, to appear as a chapter in: Graph Polynomials,
edited by M. Dehmer et al., CRC Press/Taylor & Francis Group, LL
Codes for DNA Storage Channels
We consider the problem of assembling a sequence based on a collection of its
substrings observed through a noisy channel. The mathematical basis of the
problem is the construction and design of sequences that may be discriminated
based on a collection of their substrings observed through a noisy channel. We
explain the connection between the sequence reconstruction problem and the
problem of DNA synthesis and sequencing, and introduce the notion of a DNA
storage channel. We analyze the number of sequence equivalence classes under
the channel mapping and propose new asymmetric coding techniques to combat the
effects of synthesis and sequencing noise. In our analysis, we make use of
restricted de Bruijn graphs and Ehrhart theory for rational polytopes.Comment: 32 pages, 5 figure
Gray Codes and Symmetric Chains
We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1-l,n+l], where 1 = 12