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The decomposability of additive hereditary properties of graphs

100%

Broere I., Dorfling M.

Discussiones Mathematicae Graph Theory

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2000

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tom 20

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nr 2

281-291

EN

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If 𝓟₁,...,𝓟ₙ are properties of graphs, then a (𝓟₁,...,𝓟ₙ)-decomposition of a graph G is a partition E₁,...,Eₙ of E(G) such that $G[E_i]$, the subgraph of G induced by $E_i$, is in $𝓟_i$, for i = 1,...,n. We define 𝓟₁ ⊕...⊕ 𝓟ₙ as the property {G ∈ 𝓘: G has a (𝓟₁,...,𝓟ₙ)-decomposition}. A property 𝓟 is said to be decomposable if there exist non-trivial hereditary properties 𝓟₁ and 𝓟₂ such that 𝓟 = 𝓟₁⊕ 𝓟₂. We study the decomposability of the well-known properties of graphs 𝓘ₖ, 𝓞ₖ, 𝓦ₖ, 𝓣ₖ, 𝓢ₖ, 𝓓ₖ and $𝓞 ^{p}$.

2

Generalized edge-chromatic numbers and additive hereditary properties of graphs

100%

Dorfling M., Dorfling S.

Discussiones Mathematicae Graph Theory

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2002

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tom 22

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nr 2

349-359

EN

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, 𝓘ₖ, 𝓞ₖ, 𝓦*ₖ, 𝓢ₖ and 𝓓ₖ.

3

Recognizable colorings of cycles and trees

100%

Dorfling M., Dorfling S.

Discussiones Mathematicae Graph Theory

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2012

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tom 32

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nr 1

81-90

EN

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 (a₀,a₁, ...,aₖ), where a₀ = 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 minimum k for which G has a recognizable k-coloring. In this paper we prove three conjectures of Chartrand et al. in [8] regarding the recognition number of cycles and trees.

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

3 Dorfling M.

2 Dorfling S.

1 Broere I.

1 2012

1 2002

1 2000

The decomposability of additive hereditary properties of graphs

Generalized edge-chromatic numbers and additive hereditary properties of graphs

Recognizable colorings of cycles and trees