Some Properties of Alphabet Overlap Graphs
Combinatorics
2007-05-23 v1
Abstract
Consider a graph G = G(k,d,s) with vertex set the set of all k-letter words over an alphabet of size d. An edge e = vw is in E iff v is distinct from w and the last(first) k-s letters of v are identical to the first(last) k-s letters of w. In this paper we show that G is Hamiltonian for all non-trivial values of the parameters and obtain exact values for its chromatic number when s is greater than or equal to k/2. We also obtain bounds when the chromatic number is less than k/2.
Keywords
Cite
@article{arxiv.math/0510094,
title = {Some Properties of Alphabet Overlap Graphs},
author = {Anant Godbole and Debra Knisley and Rick Norwood},
journal= {arXiv preprint arXiv:math/0510094},
year = {2007}
}