Note on the independence number of triangle-free graphs, II
Journal of Combinatorial Theory Series A
On the independence number of a graph in terms or order and size
Discrete Mathematics
Approximating Maximum Independent Set in k-Clique-Free Graphs
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Foreword: special issue on stability in graphs and related topics
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
A lower bound on independence in terms of degrees
Discrete Applied Mathematics
Partitions of graphs into small and large sets
Discrete Applied Mathematics
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We prove that if G=(V"G,E"G) is a finite, simple, and undirected graph with @k components and independence number @a(G), then there exist a positive integer k@?N and a function f:V"G-N"0 with non-negative integer values such that f(u)@?d"G(u) for u@?V"G, @a(G)=k=@?"u"@?"V"""G1d"G(u)+1-f(u), and @?"u"@?"V"""Gf(u)=2(k-@k). This result is a best possible improvement of a result due to Harant and Schiermeyer [J. Harant, I. Schiermeyer, On the independence number of a graph in terms of order and size, Discrete Math. 232 (2001) 131-138] and implies that @a(G)n(G)=2(d(G)+1+2n(G))+(d(G)+1+2n(G))^2-8 for connected graphs G of order n(G), average degree d(G), and independence number @a(G).