On a Number of Colors in Cyclically Interval Edge Colorings of Simple Cycles
نویسندگان
چکیده
منابع مشابه
On cyclically-interval edge colorings of trees
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 φ : 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 φ is a proper edge t-color...
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A proper edge-coloring of a graph G with colors 1, . . . , t is called an interval t-coloring if the colors of edges incident to any vertex of G form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, the least value of t for which G has an interval t-coloring is denoted by w(G). A graph G is ...
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An edge-coloring of a graph G with consecutive integers c1, . . . , ct is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. The set of all interval colorable graphs is denoted by N. In 2004, Giaro and...
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An edge-coloring of a graph G with colors 1, 2, . . . , t is called an interval t-coloring if for each i ∈ {1, 2, . . . , t} there is at least one edge of G colored by i, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In this paper we prove that if a connected graph G with n vertices admits an interval t-coloring, then t ≤ 2n − 3. We also show...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2013
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2013.31009