Geodesic
Unified bounds for the independence number of graphs
Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 97-117

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DOI

The Hoffman ratio bound, Lovász theta function, and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics, and information theory. By using generalized inverses and eigenvalues of graph matrices, we give bounds for independence sets and the independence number of graphs. Our bounds unify the Lovász theta function, Schrijver theta function, and Hoffman-type bounds, and we obtain the necessary and sufficient conditions of graphs attaining these bounds. Our work leads to some simple structural and spectral conditions for determining a maximum independent set, the independence number, the Shannon capacity, and the Lovász theta function of a graph.
DOI : 10.4153/S0008414X23000822
Mots-clés : Independence number, graph matrix, Lovász theta function, Shannon capacity, generalized inverse, eigenvalue 
Zhou, Jiang. Unified bounds for the independence number of graphs. Canadian journal of mathematics, Tome 77 (2025) no. 1, pp. 97-117. doi: 10.4153/S0008414X23000822
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