Graph classes: a survey
Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization
Journal of the ACM (JACM)
Recognizing cographs and threshold graphs through a classification of their edges
Information Processing Letters
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Box complexes, neighborhood complexes, and the chromatic number
Journal of Combinatorial Theory Series A
Linear colorings of simplicial complexes and collapsing
Journal of Combinatorial Theory Series A
Harmonious coloring on subclasses of colinear graphs
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology, and the framework through which it was studied, we introduce the colinear coloring on graphs. We provide an upper bound for the chromatic number χ(G), for any graph G, and show that G can be colinearly colored in polynomial time by proposing a simple algorithm. The colinear coloring of a graph G is a vertex coloring such that two vertices can be assigned the same color, if their corresponding clique sets are associated by the set inclusion relation (a clique set of a vertex u is the set of all maximal cliques containing u); the colinear chromatic number λ(G) of G is the least integer k for which G admits a colinear coloring with k colors. Based on the colinear coloring, we define the χ-colinear and α-colinear properties and characterize known graph classes in terms of these properties.