Three-Square Theorem as an Application of Andrews’ Identity
S. Bhargava, Chandrashekar Adiga, D. D. Somashekara · The Fibonacci Quarterly · 1993
For a graph G=G(V,E), a set S⊂V is k-independent if every component in the induced subgraph on S has order at most k−1. The general chromatic number χk(G) of G is the minimum order n of a partition P of the set V such that each set Vi in P is k-independent. This paper develops properties of χk(G) which generalize well-known properties of the chromatic number. Kk+1-free graphs G with χk(G)=n are constructed, and critical and minimal graphs are explored.