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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let P and Q be additive hereditary properties of graphs. The generalized chromatic number χ Q (P) is defined as follows: χ Q (P) = n iff P ⊆ Q n but P ⊆ Q n−1. We investigate the generalized chromatic numbers of the well-known… (More)

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. Let P and Q be hereditary properties of graphs. The generalized edge-chromatic number ρ Q (P) is defined as the least integer n such that P ⊆ nQ. We investigate the generalized edge-chromatic numbers of the properties → H, I k , O… (More)

For a graph G and a vertex-coloring c : V (G) → {1, 2,. .. , k}, the color code of a vertex v is the (k + 1)-tuple (a 0 , a 1 ,. .. , a k), where a 0 = c(v), and for 1 ≤ i ≤ k, a i is the number of neighbors of v colored i. A recognizable coloring is a coloring such that distinct vertices have distinct color codes. The recognition number of a graph is the… (More)

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