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Small Maximal Independent Sets and Faster Exact Graph Coloring
[article]

David Eppstein

2000
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arXiv
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pre-print

As *a* consequence, we show how to compute *the* exact *chromatic* *number* *of* *a* *graph* in time O((4/3 + 3^4/3/4)^n) = 2.4150^n, improving *a* previous O((1+3^1/3)^n) = 2.4422^n *algorithm* *of* Lawler (1976). ...
We show that, *for* any n-vertex *graph* G and integer parameter k, there are at most 3^4k-n4^n-3k maximal independent sets I ⊂ G with |I| <= k, and that all such sets can be listed in time O(3^4k-n 4^n-3k ...
It contains two results: *an* *algorithm* *for* finding *a* 3-coloring *of* *a* *graph* (if *the* *graph* is 3-*chromatic*) in time O(3 n/3 ) ≈ 1.4422 n , and *an* *algorithm* *for* finding *the* *chromatic* *number* *of* *an* arbitrary ...

arXiv:cs/0011009v1
fatcat:tcbdf2rbvnan5k7i7x2nx5ihpm