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Chromatic Sums for Colorings Avoiding Monochromatic Subgraphs

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Kubicka E., Kubicki G., McKeon K. A.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 3

541-555

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 prove an exact formulas for some graphs G. For every integer k and for every graph H, we construct families of graphs, Gk with the property that k more colors than χ (H,G) are required to realize ∑(H,G) for H-free colorings. More complexity results and constructions of graphs requiring extra colors are given for planar and outerplanar graphs.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Kubicka E.

1 Kubicki G.

1 McKeon K. A.

1 2015

Wyniki wyszukiwania

Chromatic Sums for Colorings Avoiding Monochromatic Subgraphs