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Investigation on Interval Edge-Colorings of Graphs

✍ Scribed by A.S. Asratian; R.R. Kamalian

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 380 KB
Volume: 62
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1994.1053

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✦ Synopsis

An edge-coloring of a simple graph (G) with colors (1,2, \ldots, t) is called an interval (t)-coloring [3] if at least one edge of (G) is colored by color (i, i=1, \ldots, t) and the edges incident with each vertex (x) are colored by (d_{G}(x)) consecutive colors, where (d_{G}(x)) is the degree of the vertex (x). In this paper we investigate some properties of interval colorings and their variations. It is proved, in particular, that if a simple graph (G=(V, E)) without triangles has an interval (t)-coloring, then (t \leqslant|V|-1). (ิ) 1994 Academic Press. Inc.

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