A graph G(a, k, t) is called an alphabet overlap graph where a, k, and t are positive integers such that 0 ≤ t < k and the vertex set V of G is defined as, V = {v : v = (v1v2...vk); vi ∊ {1, 2, ..., a}, (1 ≤ i ≤ k)}. That is, each vertex, v, is a word of length k over an alphabet of size a. There exists an edge between two vertices u, v if and only if the last t letters in u equal the first t letters in v or the first t letters in u equal the last t letters in v. We determine the chromatic number of G(a, k, t) for all k ≥ 3, t = k − 2, and a = 2; except when k = 7, 8, 9, and 11.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-3491 |
| Date | 15 December 2007 |
| Creators | Farley, Jerry Brent |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
| Rights | Copyright by the authors. |
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