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- Strong_coloring abstract "In graph theory, a strong coloring, with respect to a partition of the vertices into (disjoint) subsets of equal sizes, is a (proper) vertex coloring in which every color appears exactly once in every partition.When the order of the graph G is not divisible by k, we add isolated vertices to G just enough to make the order of the new graph G′ divisible by k.In that case, a strong coloring of G′ minus the previously added isolated vertices is considered a strong coloring of G.A graph is strongly k-colorable if, for each partition of the vertices into sets of size k, it admits a strong coloring.The strong chromatic number sχ(G) of a graph G is the least k such that G is strongly k-colorable.A graph is strongly k-chromatic if it has strong chromatic number k.Some properties of sχ(G): sχ(G) > Δ(G). sχ(G) ≤ 3 Δ(G) − 1 (Haxell) Asymptotically, sχ(G) ≤ 11 Δ(G) / 4 + o(Δ(G)). (Haxell)Here Δ(G) is the maximum degree.Strong chromatic number was independently introduced by Alon (1988) and Fellows (1990).".
- Strong_coloring thumbnail Strong_coloring_sample.svg?width=300.
- Strong_coloring wikiPageID "690775".
- Strong_coloring wikiPageRevisionID "536925103".
- Strong_coloring hasPhotoCollection Strong_coloring.
- Strong_coloring subject Category:Graph_coloring.
- Strong_coloring comment "In graph theory, a strong coloring, with respect to a partition of the vertices into (disjoint) subsets of equal sizes, is a (proper) vertex coloring in which every color appears exactly once in every partition.When the order of the graph G is not divisible by k, we add isolated vertices to G just enough to make the order of the new graph G′ divisible by k.In that case, a strong coloring of G′ minus the previously added isolated vertices is considered a strong coloring of G.A graph is strongly k-colorable if, for each partition of the vertices into sets of size k, it admits a strong coloring.The strong chromatic number sχ(G) of a graph G is the least k such that G is strongly k-colorable.A graph is strongly k-chromatic if it has strong chromatic number k.Some properties of sχ(G): sχ(G) > Δ(G). ".
- Strong_coloring label "Strong coloring".
- Strong_coloring sameAs m.0332xv.
- Strong_coloring sameAs Q7624545.
- Strong_coloring sameAs Q7624545.
- Strong_coloring wasDerivedFrom Strong_coloring?oldid=536925103.
- Strong_coloring depiction Strong_coloring_sample.svg.
- Strong_coloring isPrimaryTopicOf Strong_coloring.