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arXiv · 1912.01546

On the deficiency of complete multipartite graphs

Armen R. Davtyan·Gevorg M. Minasyan·Petros A. Petrosyan
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Abstract

An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is an \emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an integer interval. It is well-known that there are graphs that do not have interval colorings. The \emph{deficiency} of a graph $G$, denoted by $\mathrm{def}(G)$, is the minimum number of pendant edges whose attachment to $G$ leads to a graph admitting an interval coloring. In this paper we investigate the problem of determining or bounding of the deficiency of complete multipartite graphs. In particular, we obtain a tight upper bound for the deficiency of complete multipartite graphs. We also determine or bound the deficiency for some classes of complete multipartite graphs.

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Armen R. Davtyan, Gevorg M. Minasyan, Petros A. Petrosyan. 2019-12-03. On the deficiency of complete multipartite graphs. https://arxiv.org/abs/1912.01546

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