Cocoloring - Wikipedia
WEBIn graph theory, a cocoloring of a graph G is an assignment of colors to the vertices such that each color class forms an independent set in G or in the complement of G. The cochromatic number z(G) of G is the fewest colors needed in any cocolorings of G.
Fractional Cocoloring of Graphs | Graphs and Combinatorics
WEBMar 14, 2022 · A labeling is an assignment of nonnegative numbers to each vertex. A color labeling is an assignment where the labels on each independent set sum to at most one. A cocolor labeling is an assignment where the sum across each clique and independent set is …
Some of My Favorite Coloring Problems for Graphs and Digraphs
WEBOct 20, 2016 · A coloring is simply a partition of the vertex set into parts, each of which induces a graph having a given property. For example, in the most studied form of coloring, each part induces an empty graph. I will refer to this as a traditional coloring.
WEBCombining these two concepts we have introduces two new types of cocoloring viz, dominating cocoloring and -cocoloring. A dominating cocoloring of is a cocoloring of such that atleast one of the sets in the partition is a dominating set. Hence dominating cocoloring is a conditional cocoloring.
5.8: Graph Coloring - Mathematics LibreTexts
WEBGraph coloring is closely related to the concept of an independent set. Definition 5.8.2: Independent. A set S of vertices in a graph is independent if no two vertices of S are adjacent. If a graph is properly colored, the vertices that are assigned a particular color form an independent set.
[1906.05504] Fractional cocoloring of graphs - arXiv.org
WEBJun 13, 2019 · Fractional cocoloring of graphs. The cochromatic number of a graph is the fewest number of colors needed to color the vertices of so that each color class is a clique or an independent set.
Fixed-parameter algorithms for the cocoloring problem
WEBApr 20, 2014 · A (k, l)-cocoloring is a cocoloring with at most k colors inducing stable sets and at most ℓ colors inducing cliques. Given a graph G and positive integers k and ℓ , the Cocoloring Problem is the problem of deciding whether G is ( k , ℓ ) -cocolorable.
Fractional Cocoloring of Graphs - ResearchGate
WEBJun 1, 2022 · Abstract. The cochromatic number Z (G) of a graph G is the fewest number of colors needed to color the vertices of G so that each color class is a clique or an independent set.
Dominating Cocoloring of Graphs - ResearchGate
WEBNov 30, 2019 · A -cocolouring of a graph is a partition of the vertex set into subsets such that each set induces either a clique or an independent set in . The cochromatic number of a graph is the least such...
WEBAn acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of …
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