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- Harmonious_coloring abstract "In graph theory, a harmonious coloring is a (proper) vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number χH(G) of a graph G is the minimum number of colors needed for any harmonious coloring of G.Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color; thus χH(G) ≤ |V(G)|. There trivially exist graphs G with χH(G) > χ(G) (where χ is the chromatic number); one example is the path of length 2, which can be 2-colored but has no harmonious coloring with 2 colors.Some properties of χH(G): χH(Tk,3) = ⌈(3/2)(k+1)⌉, where Tk,3 is the complete k-ary tree with 3 levels. (Mitchem 1989)Harmonious coloring was first proposed by Harary and Plantholt (1982).Still very little is known about it.".
- Harmonious_coloring thumbnail Harmonious_coloring_tree.svg?width=300.
- Harmonious_coloring wikiPageExternalLink biblio.html.
- Harmonious_coloring wikiPageID "690728".
- Harmonious_coloring wikiPageRevisionID "517632169".
- Harmonious_coloring hasPhotoCollection Harmonious_coloring.
- Harmonious_coloring subject Category:Graph_coloring.
- Harmonious_coloring comment "In graph theory, a harmonious coloring is a (proper) vertex coloring in which every pair of colors appears on at most one pair of adjacent vertices. The harmonious chromatic number χH(G) of a graph G is the minimum number of colors needed for any harmonious coloring of G.Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color; thus χH(G) ≤ |V(G)|.".
- Harmonious_coloring label "Harmonious coloring".
- Harmonious_coloring label "Гармоническая раскраска".
- Harmonious_coloring sameAs m.0332qn.
- Harmonious_coloring sameAs Q5659354.
- Harmonious_coloring sameAs Q5659354.
- Harmonious_coloring wasDerivedFrom Harmonious_coloring?oldid=517632169.
- Harmonious_coloring depiction Harmonious_coloring_tree.svg.
- Harmonious_coloring isPrimaryTopicOf Harmonious_coloring.