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On Interval Non-Edge-Colorable Eulerian Multigraphs (1311.2210v2)
Published 9 Nov 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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