A note on interval edge-colorings of graphs

Details A note on interval edge-colorings of graphs A note on interval edge-colorings of graphs

2010-07-10

arxiv.org/abs/1007.1717v2

Computer Science

Discrete Mathematics

4 pages, minor changes

Scientific paper

An edge-coloring of a graph $G$ with colors $1,2,\ldots,t$ is called an interval $t$-coloring if for each $i\in \{1,2,\ldots,t\}$ 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 $t\leq 2n-3$. We also show that if $G$ is a connected $r$-regular graph with $n$ vertices has an interval $t$-coloring and $n\geq 2r+2$, then this upper bound can be improved to $2n-5$.

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