Displaying similar documents to “Polynomial-time partition of a graph into cliques.”

Combinatorial interpretations for identities using chromatic partitions

Mateus Alegri, Wagner Ferreira Santos, Samuel Brito Silva (2021)

Czechoslovak Mathematical Journal

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We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities.

The B-Domatic Number of a Graph

Odile Favaron (2013)

Discussiones Mathematicae Graph Theory

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Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the counterpart...