A note on upper bounds for the maximum span in interval edge-colorings of graphs

An edge-coloring of a graph G with colors 1,…,t is an intervalt-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. In 1994, Asratian and Kamalian proved that if a connected graph G admits an interval t-coloring, then t...

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Bibliographic Details
Published inDiscrete mathematics Vol. 312; no. 8; pp. 1393 - 1399
Main Authors Kamalian, R.R., Petrosyan, P.A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 28.04.2012
Subjects
Bipartite graph
Diameter
Edge-coloring
Graphs
Integers
Interval coloring
Intervals
Mathematical analysis
Upper bounds
Edge-coloring
Interval coloring
Bipartite graph
Diameter
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Summary:An edge-coloring of a graph G with colors 1,…,t is an intervalt-coloring if all colors are used, and the colors of edges incident to each vertex of G are distinct and form an interval of integers. In 1994, Asratian and Kamalian proved that if a connected graph G admits an interval t-coloring, then t≤(diam(G)+1)(Δ(G)−1)+1, and if G is also bipartite, then this upper bound can be improved to t≤diam(G)(Δ(G)−1)+1, where Δ(G) is the maximum degree of G and diam(G) is the diameter of G. In this note, we show that these upper bounds cannot be significantly improved.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.01.005