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## Discussiones Mathematicae Graph Theory

2011 | 31 | 2 | 357-373
Tytuł artykułu

### Interval edge colorings of some products of graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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. A graph G is interval colorable, if there is an integer t ≥ 1 for which G has an interval t-coloring. Let ℜ be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if G,H ∈ 𝔑, then the Cartesian product of these graphs belongs to 𝔑. Also, they formulated a similar problem for the lexicographic product as an open problem. In this paper we first show that if G ∈ 𝔑, then G[nK₁] ∈ 𝔑 for any n ∈ ℕ. Furthermore, we show that if G,H ∈ 𝔑 and H is a regular graph, then strong and lexicographic products of graphs G,H belong to 𝔑. We also prove that tensor and strong tensor products of graphs G,H belong to 𝔑 if G ∈ 𝔑 and H is a regular graph.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
357-373
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-11-20
poprawiono
2010-06-29
zaakceptowano
2010-07-02
Twórcy
autor
• Institute for Informatics and Automation Problems, National Academy of Sciences, 0014, Armenia
• Department of Informatics and Applied Mathematics, Yerevan State University, 0025, Armenia
Bibliografia
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• [4] A.S. Asratian, C.J. Casselgren, J. Vandenbussche and D.B. West, Proper path-factors and interval edge-coloring of (3,4)-biregular bigraphs, J. Graph Theory 61 (2009) 88-97, doi: 10.1002/jgt.20370.
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Bibliografia
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