Abstract
Computing the independence number of a graph remains NP-hard, even restricted to the class of triangle-free graphs. So the question arises, whether this remains valid if the minimum degree is required to be large. While in general graphs this problem remains NP-hard even within the class of graphs with minimum degree δ > (1 − ε)n, the situation is different for triangle-free graphs. It will be shown that for triangle-free graphs with δ > n/3 the independence number can be computed as fast as matrix multiplication, while within the class of triangle-free graphs with δ > (1-ε)n/4 the problem is already NP-hard.
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© 1997 Springer-Verlag Berlin Heidelberg
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Brandt, S. (1997). Computing the independence number of dense triangle-free graphs. In: Möhring, R.H. (eds) Graph-Theoretic Concepts in Computer Science. WG 1997. Lecture Notes in Computer Science, vol 1335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024491
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DOI: https://doi.org/10.1007/BFb0024491
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