On cyclically-interval edge colorings of trees
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KAMALIAN, Rafayel. On cyclically-interval edge colorings of trees. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2012, nr. 1(68), pp. 50-58. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1(68) / 2012 / ISSN 1024-7696 /ISSNe 2587-4322

On cyclically-interval edge colorings of trees

Pag. 50-58

Kamalian Rafayel
 
 
Disponibil în IBN: 6 decembrie 2013


Rezumat

For an undirected, simple, finite, connected graph G, we denote by V (G) and E(G) the sets of its vertices and edges, respectively. A function ' : E(G) → {1, 2, . . . , t} is called a proper edge t-coloring of a graph G if adjacent edges are colored differently and each of t colors is used. An arbitrary nonempty subset of consecutive integers is called an interval. If ' is a proper edge t-coloring of a graph G and x ∈ V (G), then SG(x, ') denotes the set of colors of edges of G which are incident with x. A proper edge t-coloring ' of a graph G is called a cyclically-interval t-coloring if for any x ∈ V (G) at least one of the following two conditions holds: a) SG(x,') is an interval, b) {1, 2, . . . , t} \ SG(x, ') is an interval. For any t ∈ N, let Mt be the set of graphs for which there exists a cyclically-interval t-coloring, and let M ≡St≥1 Mt. For an arbitrary tree G, it is proved that G ∈ M and all possible values of t are found for which G ∈ Mt.

Cuvinte-cheie
Tree,

interval edge coloring, cyclically-interval edge coloring.