The chromatic sum of a graph: history and recent developments.
Chromatic Sums for Colorings Avoiding Monochromatic Subgraphs
Given graphs G and H, a vertex coloring c : V (G) →ℕ is an H-free coloring of G if no color class contains a subgraph isomorphic to H. The H-free chromatic number of G, χ (H,G), is the minimum number of colors in an H-free coloring of G. The H-free chromatic sum of G, ∑(H,G), is the minimum value achieved by summing the vertex colors of each H-free coloring of G. We provide a general bound for ∑(H,G), discuss the computational complexity of finding this parameter for different choices of H, and...
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