We examine the problem of counting interval graphs. We answer the question posed by Hanlon, of whether the formal power series generating function of the number of interval graphs on n vertices has a positive radius of convergence. We have found that it is zero. We have obtained a lower bound and an upper bound on the number of interval graphs on n vertices. We also study the application of interval graphs to the dynamic storage allocation problem. Dynamic storage allocation has been shown to be NP-complete by Stockmeyer. Coloring interval graphs on-line has applications to dynamic storage allocation. The most colors used by Kierstead's algorithm is 3 ω -2, where ω is the size of the largest clique in the graph. We determine a lower bound on the colors used. One such lower bound is 2 ω -1.
Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1079 |
Date | 01 January 2016 |
Creators | Yang, Joyce C |
Publisher | Scholarship @ Claremont |
Source Sets | Claremont Colleges |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | HMC Senior Theses |
Rights | © 2016 Joyce C Yang, default |
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