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2015 | 35 | 3 | 541-555
Tytuł artykułu

Chromatic Sums for Colorings Avoiding Monochromatic Subgraphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
35
Numer
3
Strony
541-555
Opis fizyczny
Daty
wydano
2015-08-01
otrzymano
2013-02-27
poprawiono
2014-11-10
zaakceptowano
2014-11-10
online
2015-07-29
Twórcy
autor
Bibliografia
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Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1819
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