Emergent Mind
On Interval Non-Edge-Colorable Eulerian Multigraphs
(1311.2210)
Published Nov 9, 2013
in
math.CO
and
cs.DM
Abstract
An edge-coloring of a multigraph $G$ with colors $1,\ldots,t$ is called an interval $t$-coloring if all colors are used, and the colors of edges incident to any vertex of $G$ are distinct and form an interval of integers. In this note, we show that all Eulerian multigraphs with an odd number of edges have no interval coloring. We also give some methods for constructing of interval non-edge-colorable Eulerian multigraphs.
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