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non-approximation
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On the Computational Complexity of Graph Problems
, M.Sc. Thesis Sharif University of Technology ; Jafari, Amir (Supervisor)
Abstract
Computational complexity of graph problems is an important branch in the-oretical computer science. We introduce to some of ideas for computing the complexity of graph problems with some kind and beautiful examples. Next, we show hardness and inapproximability of some problems. Representation number of graphs has been introduce by Pavel Erdos by Number theory. We prove n1−ϵ inapproximability of that. Lucky number η has been studied by Grytczuk et.al . We show for planar and 3-colorable graphs, it is NP-Complete whether η = 2. Note that since a conjecture, for those graphs, 2 ≤ η ≤ 3. Also for each k ≥ 2, we show NP-completeness of η ≤ k for the graphs. Proper orientation number −→ is a...